Abstract group data - 46656.ir

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• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_abelian	boolean
  aut_cyclic	boolean
  aut_derived_length	smallint
  aut_exponent	numeric
  aut_gen_orders	numeric[]
  aut_gens	numeric[]
  aut_group	text
  aut_hash	bigint
  aut_nilpotency_class	smallint
  aut_nilpotent	boolean
  aut_order	numeric
  aut_permdeg	integer
  aut_perms	numeric[]
  aut_phi_ratio	double precision
  aut_solvable	boolean
  aut_stats	numeric[]
  aut_supersolvable	boolean
  aut_tex	text
  autcent_abelian	boolean
  autcent_cyclic	boolean
  autcent_exponent	numeric
  autcent_group	text
  autcent_hash	bigint
  autcent_nilpotent	boolean
  autcent_order	numeric
  autcent_solvable	boolean
  autcent_split	boolean
  autcent_supersolvable	boolean
  autcent_tex	text
  autcentquo_abelian	boolean
  autcentquo_cyclic	boolean
  autcentquo_exponent	numeric
  autcentquo_group	text
  autcentquo_hash	bigint
  autcentquo_nilpotent	boolean
  autcentquo_order	numeric
  autcentquo_solvable	boolean
  autcentquo_supersolvable	boolean
  autcentquo_tex	text
  cc_stats	numeric[]
  center_label	text
  center_order	numeric
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  conjugacy_classes_known	boolean
  counter	integer
  cyclic	boolean
  derived_length	smallint
  dihedral	boolean
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  familial	boolean
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  inner_abelian	boolean
  inner_cyclic	boolean
  inner_exponent	numeric
  inner_gen_orders	numeric[]
  inner_gens	numeric[]
  inner_hash	bigint
  inner_nilpotent	boolean
  inner_order	numeric
  inner_split	boolean
  inner_tex	text
  inner_used	smallint[]
  irrC_degree	integer
  irrQ_degree	integer
  irrQ_dim	integer
  irrR_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_count	numeric
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  linQ_degree_count	numeric
  linQ_dim	integer
  linQ_dim_count	numeric
  linR_count	numeric
  linR_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_abelian	boolean
  outer_cyclic	boolean
  outer_equivalence	boolean
  outer_exponent	numeric
  outer_gen_orders	numeric[]
  outer_gen_pows	numeric[]
  outer_gens	numeric[]
  outer_group	text
  outer_hash	bigint
  outer_nilpotent	boolean
  outer_order	numeric
  outer_permdeg	integer
  outer_perms	numeric[]
  outer_solvable	boolean
  outer_supersolvable	boolean
  outer_tex	text
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [12, 36, 36, 12, 12], 'aut_gens': [[6227827207, 94494037865, 101201068405], [6227389189, 461482520349, 467230579635], [443130957699, 536532681572, 363565923944], [549099855751, 554364887012, 467081435790], [443758740204, 556284159258, 288957720344], [542760342204, 716634294365, 374104246668]], 'aut_group': None, 'aut_hash': 4954454136060197193, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 186624, 'aut_permdeg': 45, 'aut_perms': [58035254216799252249215281391136323590025299485348858211, 29420706275574493657549338584831744885550395262120493762, 43919862015121936140470770123345731212264295149898845341, 17679937733144046531067764679167217341092510501103094608, 23859245498024408034007839100699805084686138374891538831], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 18, 1, 1], [2, 27, 1, 2], [2, 54, 1, 1], [2, 81, 1, 1], [2, 162, 1, 1], [2, 243, 1, 2], [2, 486, 1, 1], [3, 4, 2, 1], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 24, 2, 1], [3, 32, 2, 1], [3, 48, 2, 1], [3, 72, 1, 1], [3, 288, 2, 1], [4, 9, 2, 1], [4, 54, 1, 1], [4, 81, 2, 1], [4, 162, 1, 1], [4, 162, 2, 1], [4, 243, 2, 2], [4, 486, 1, 1], [4, 486, 2, 2], [4, 1458, 1, 1], [4, 1458, 2, 1], [6, 36, 1, 4], [6, 36, 2, 1], [6, 54, 1, 2], [6, 72, 1, 2], [6, 72, 2, 1], [6, 108, 1, 2], [6, 108, 2, 2], [6, 144, 2, 4], [6, 216, 1, 1], [6, 216, 2, 2], [6, 288, 2, 1], [6, 324, 1, 4], [6, 432, 2, 1], [6, 486, 1, 1], [6, 648, 1, 2], [6, 864, 2, 1], [6, 972, 1, 1], [6, 1944, 1, 1], [9, 144, 1, 1], [9, 576, 2, 1], [12, 54, 2, 1], [12, 72, 2, 1], [12, 108, 1, 1], [12, 108, 2, 1], [12, 216, 2, 1], [12, 324, 2, 4], [12, 432, 2, 1], [12, 486, 2, 1], [12, 648, 2, 3], [12, 972, 1, 1], [12, 972, 2, 2], [12, 1944, 2, 1], [18, 1296, 1, 1], [36, 1296, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^5.A_4.C_8.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': None, 'autcentquo_hash': 4954454136060197193, 'autcentquo_nilpotent': False, 'autcentquo_order': 186624, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^5.A_4.C_8.C_2^3', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 18, 1], [2, 27, 2], [2, 54, 1], [2, 81, 1], [2, 162, 1], [2, 243, 2], [2, 486, 1], [3, 4, 2], [3, 6, 1], [3, 8, 1], [3, 12, 1], [3, 24, 2], [3, 32, 2], [3, 48, 2], [3, 72, 1], [3, 288, 2], [4, 9, 2], [4, 54, 1], [4, 81, 2], [4, 162, 3], [4, 243, 4], [4, 486, 5], [4, 1458, 3], [6, 36, 6], [6, 54, 2], [6, 72, 4], [6, 108, 6], [6, 144, 8], [6, 216, 5], [6, 288, 2], [6, 324, 4], [6, 432, 2], [6, 486, 1], [6, 648, 2], [6, 864, 2], [6, 972, 1], [6, 1944, 1], [9, 144, 1], [9, 576, 2], [12, 54, 2], [12, 72, 2], [12, 108, 3], [12, 216, 2], [12, 324, 8], [12, 432, 2], [12, 486, 2], [12, 648, 6], [12, 972, 5], [12, 1944, 2], [18, 1296, 1], [36, 1296, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '46656.ir', 'commutator_count': 1, 'commutator_label': '2916.kw', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 226, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['1296.3490', 1], ['36.9', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 18, 1, 1], [2, 27, 1, 2], [2, 54, 1, 1], [2, 81, 1, 1], [2, 162, 1, 1], [2, 243, 1, 2], [2, 486, 1, 1], [3, 4, 1, 2], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 24, 1, 2], [3, 32, 1, 2], [3, 48, 1, 2], [3, 72, 1, 1], [3, 288, 1, 2], [4, 9, 2, 1], [4, 54, 1, 1], [4, 81, 2, 1], [4, 162, 1, 1], [4, 162, 2, 1], [4, 243, 2, 2], [4, 486, 1, 1], [4, 486, 2, 2], [4, 1458, 1, 1], [4, 1458, 2, 1], [6, 36, 1, 6], [6, 54, 1, 2], [6, 72, 1, 4], [6, 108, 1, 6], [6, 144, 1, 8], [6, 216, 1, 5], [6, 288, 1, 2], [6, 324, 1, 4], [6, 432, 1, 2], [6, 486, 1, 1], [6, 648, 1, 2], [6, 864, 1, 2], [6, 972, 1, 1], [6, 1944, 1, 1], [9, 144, 1, 1], [9, 576, 1, 2], [12, 54, 2, 1], [12, 72, 2, 1], [12, 108, 1, 1], [12, 108, 2, 1], [12, 216, 1, 2], [12, 324, 2, 4], [12, 432, 1, 2], [12, 486, 2, 1], [12, 648, 1, 2], [12, 648, 2, 2], [12, 972, 1, 1], [12, 972, 2, 2], [12, 1944, 2, 1], [18, 1296, 1, 1], [36, 1296, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 146764800, 'exponent': 36, 'exponents_of_order': [6, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 8], [32, 1, 4], [48, 1, 10], [64, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '46656.ir', 'hash': 9168954550374180198, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [2, 12, 12], 'inner_gens': [[6227827207, 193724617120, 212887952378], [443758740025, 94494037865, 275985567075], [180677997829, 188861989840, 101201068405]], 'inner_hash': 9168954550374180198, 'inner_nilpotent': False, 'inner_order': 46656, 'inner_split': False, 'inner_tex': 'C_3:S_3^4.D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 16], [2, 8], [3, 16], [4, 8], [6, 16], [8, 12], [12, 28], [16, 4], [24, 8], [32, 4], [48, 10], [64, 2]], 'label': '46656.ir', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3:S3^4.D6', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 88, 'number_characteristic_subgroups': 56, 'number_conjugacy_classes': 132, 'number_divisions': 110, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 3725, 'number_subgroup_classes': 4970, 'number_subgroups': 860936, 'old_label': None, 'order': 46656, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1359], [3, 890], [4, 8496], [6, 12654], [9, 1296], [12, 18072], [18, 1296], [36, 2592]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 190], 'outer_gens': [[87309654099, 697434676509, 287002598725], [6227827514, 94015399565, 108907948904]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [3, 8], [4, 10], [6, 12], [8, 8], [12, 22], [16, 4], [24, 13], [32, 5], [48, 10], [64, 2]], 'representations': {'PC': {'code': '358675344744367769133843535757047509686320414200740099217737416133201649255177009936167077881944382047453400819404948927961566670213393874642944629750975379211603415694513360162177997480692343976306033543711072256899146698813783', 'gens': [1, 2, 5, 7, 9, 11, 12], 'pres': [12, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 478368, 1008817, 61, 1083314, 98, 1186179, 865444, 1362256, 116308, 237280, 172, 376721, 1757, 3525990, 1027170, 618438, 114198, 50958, 246, 165895, 668179, 995359, 20779, 43831, 4230152, 278660, 680432, 488960, 42824, 30536, 320, 1313289, 1249941, 164193, 544365, 69177, 11601, 348502, 342178, 767255, 311075, 103727, 31187, 5291]}, 'Perm': {'d': 15, 'gens': [6227827207, 94494037865, 101201068405]}}, 'schur_multiplier': [2, 2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3:S_3^4.D_6', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 162663286
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 226, 'group_order': 46656, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 162663330
    {'aut_label': '2A', 'centralizer': '9.a1', 'counter': 2, 'group_counter': 226, 'group_order': 46656, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 40320, 'size': 9}
  • id: 162663341
    {'aut_label': '2B', 'centralizer': '9.b1', 'counter': 3, 'group_counter': 226, 'group_order': 46656, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 7, 'size': 9}
  • id: 162663352
    {'aut_label': '2C', 'centralizer': '18.e1', 'counter': 4, 'group_counter': 226, 'group_order': 46656, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 46551420720, 'size': 18}
  • id: 162663363
    {'aut_label': '2D', 'centralizer': '27.a1', 'counter': 5, 'group_counter': 226, 'group_order': 46656, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 41091120, 'size': 27}
  • id: 162663374
    {'aut_label': '2E', 'centralizer': '27.b1', 'counter': 6, 'group_counter': 226, 'group_order': 46656, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 39957120, 'size': 27}
  • id: 162663385
    {'aut_label': '2F', 'centralizer': '54.a1', 'counter': 7, 'group_counter': 226, 'group_order': 46656, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 46591337520, 'size': 54}
  • id: 162663396
    {'aut_label': '2G', 'centralizer': '81.b1', 'counter': 8, 'group_counter': 226, 'group_order': 46656, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 355459104314, 'size': 81}
  • id: 162663407
    {'aut_label': '2H', 'centralizer': '162.m1', 'counter': 9, 'group_counter': 226, 'group_order': 46656, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 549099855804, 'size': 162}
  • id: 162663287
    {'aut_label': '2I', 'centralizer': '243.b1', 'counter': 10, 'group_counter': 226, 'group_order': 46656, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 41051114, 'size': 243}
  • id: 162663298
    {'aut_label': '2J', 'centralizer': '243.a1', 'counter': 11, 'group_counter': 226, 'group_order': 46656, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 34136852511, 'size': 243}
  • id: 162663309
    {'aut_label': '2K', 'centralizer': '486.a1', 'counter': 12, 'group_counter': 226, 'group_order': 46656, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 549100218351, 'size': 486}
  • id: 162663320
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 13, 'group_counter': 226, 'group_order': 46656, 'label': '3A', 'order': 3, 'powers': [13, 1], 'representative': 104, 'size': 4}
  • id: 162663324
    {'aut_label': '3A', 'centralizer': '4.b1', 'counter': 14, 'group_counter': 226, 'group_order': 46656, 'label': '3B', 'order': 3, 'powers': [14, 1], 'representative': 458, 'size': 4}
  • id: 162663325
    {'aut_label': '3C', 'centralizer': '6.f1', 'counter': 15, 'group_counter': 226, 'group_order': 46656, 'label': '3C', 'order': 3, 'powers': [15, 1], 'representative': 2917600560, 'size': 6}
  • id: 162663326
    {'aut_label': '3D', 'centralizer': '8.i1', 'counter': 16, 'group_counter': 226, 'group_order': 46656, 'label': '3D', 'order': 3, 'powers': [16, 1], 'representative': 295664181120, 'size': 8}
  • id: 162663327
    {'aut_label': '3E', 'centralizer': '12.d1', 'counter': 17, 'group_counter': 226, 'group_order': 46656, 'label': '3E', 'order': 3, 'powers': [17, 1], 'representative': 34096648320, 'size': 12}
  • id: 162663328
    {'aut_label': '3F', 'centralizer': '24.s1', 'counter': 18, 'group_counter': 226, 'group_order': 46656, 'label': '3F', 'order': 3, 'powers': [18, 1], 'representative': 2917600664, 'size': 24}
  • id: 162663329
    {'aut_label': '3F', 'centralizer': '24.s1', 'counter': 19, 'group_counter': 226, 'group_order': 46656, 'label': '3G', 'order': 3, 'powers': [19, 1], 'representative': 2917601018, 'size': 24}
  • id: 162663331
    {'aut_label': '3H', 'centralizer': '32.b1', 'counter': 20, 'group_counter': 226, 'group_order': 46656, 'label': '3H', 'order': 3, 'powers': [20, 1], 'representative': 382729979790, 'size': 32}
  • id: 162663332
    {'aut_label': '3H', 'centralizer': '32.b1', 'counter': 21, 'group_counter': 226, 'group_order': 46656, 'label': '3I', 'order': 3, 'powers': [21, 1], 'representative': 387999647715, 'size': 32}
  • id: 162663333
    {'aut_label': '3J', 'centralizer': '48.f1', 'counter': 22, 'group_counter': 226, 'group_order': 46656, 'label': '3J', 'order': 3, 'powers': [22, 1], 'representative': 34096648424, 'size': 48}
  • id: 162663334
    {'aut_label': '3J', 'centralizer': '48.f1', 'counter': 23, 'group_counter': 226, 'group_order': 46656, 'label': '3K', 'order': 3, 'powers': [23, 1], 'representative': 34096648778, 'size': 48}
  • id: 162663335
    {'aut_label': '3L', 'centralizer': '72.dw1', 'counter': 24, 'group_counter': 226, 'group_order': 46656, 'label': '3L', 'order': 3, 'powers': [24, 1], 'representative': 174564190080, 'size': 72}
  • id: 162663336
    {'aut_label': '3M', 'centralizer': '288.bb1', 'counter': 25, 'group_counter': 226, 'group_order': 46656, 'label': '3M', 'order': 3, 'powers': [25, 1], 'representative': 719148689664, 'size': 288}
  • id: 162663337
    {'aut_label': '3M', 'centralizer': '288.bb1', 'counter': 26, 'group_counter': 226, 'group_order': 46656, 'label': '3N', 'order': 3, 'powers': [26, 1], 'representative': 700352317178, 'size': 288}
  • id: 162663338
    {'aut_label': '4A1', 'centralizer': '9.b1', 'counter': 27, 'group_counter': 226, 'group_order': 46656, 'label': '4A1', 'order': 4, 'powers': [3, 28], 'representative': 142, 'size': 9}
  • id: 162663339
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    {'aut_label': '12P1', 'centralizer': '648.eo1', 'counter': 119, 'group_counter': 226, 'group_order': 46656, 'label': '12P1', 'order': 12, 'powers': [88, 28], 'representative': 174564190698, 'size': 648}
  • id: 162663310
    {'aut_label': '12P1', 'centralizer': '648.eo1', 'counter': 120, 'group_counter': 226, 'group_order': 46656, 'label': '12P-1', 'order': 12, 'powers': [88, 27], 'representative': 93576274025, 'size': 648}
  • id: 162663311
    {'aut_label': '12Q1', 'centralizer': '648.ds1', 'counter': 121, 'group_counter': 226, 'group_order': 46656, 'label': '12Q1', 'order': 12, 'powers': [58, 33], 'representative': 394704616868, 'size': 648}
  • id: 162663312
    {'aut_label': '12Q1', 'centralizer': '648.ds1', 'counter': 122, 'group_counter': 226, 'group_order': 46656, 'label': '12Q-1', 'order': 12, 'powers': [58, 34], 'representative': 288958486882, 'size': 648}
  • id: 162663313
    {'aut_label': '12R', 'centralizer': '972.cq1', 'counter': 123, 'group_counter': 226, 'group_order': 46656, 'label': '12R', 'order': 12, 'powers': [54, 39], 'representative': 631857905671, 'size': 972}
  • id: 162663314
    {'aut_label': '12S1', 'centralizer': '972.a1', 'counter': 124, 'group_counter': 226, 'group_order': 46656, 'label': '12S1', 'order': 12, 'powers': [62, 40], 'representative': 106510038244, 'size': 972}
  • id: 162663315
    {'aut_label': '12S1', 'centralizer': '972.a1', 'counter': 125, 'group_counter': 226, 'group_order': 46656, 'label': '12S-1', 'order': 12, 'powers': [62, 41], 'representative': 610887836320, 'size': 972}
  • id: 162663316
    {'aut_label': '12T1', 'centralizer': '972.cq1', 'counter': 126, 'group_counter': 226, 'group_order': 46656, 'label': '12T1', 'order': 12, 'powers': [86, 42], 'representative': 549945734219, 'size': 972}
  • id: 162663317
    {'aut_label': '12T1', 'centralizer': '972.cq1', 'counter': 127, 'group_counter': 226, 'group_order': 46656, 'label': '12T-1', 'order': 12, 'powers': [86, 43], 'representative': 544828395538, 'size': 972}
  • id: 162663318
    {'aut_label': '12U1', 'centralizer': '1944.df1', 'counter': 128, 'group_counter': 226, 'group_order': 46656, 'label': '12U1', 'order': 12, 'powers': [88, 35], 'representative': 94494038253, 'size': 1944}
  • id: 162663319
    {'aut_label': '12U1', 'centralizer': '1944.df1', 'counter': 129, 'group_counter': 226, 'group_order': 46656, 'label': '12U-1', 'order': 12, 'powers': [88, 36], 'representative': 436092129332, 'size': 1944}
  • id: 162663321
    {'aut_label': '18A', 'centralizer': '1296.ee1', 'counter': 130, 'group_counter': 226, 'group_order': 46656, 'label': '18A', 'order': 18, 'powers': [93, 58], 'representative': 556171666231, 'size': 1296}
  • id: 162663322
    {'aut_label': '36A1', 'centralizer': '1296.ee1', 'counter': 131, 'group_counter': 226, 'group_order': 46656, 'label': '36A1', 'order': 36, 'powers': [130, 98], 'representative': 722861718299, 'size': 1296}
  • id: 162663323
    {'aut_label': '36A1', 'centralizer': '1296.ee1', 'counter': 132, 'group_counter': 226, 'group_order': 46656, 'label': '36A-1', 'order': 36, 'powers': [130, 99], 'representative': 623823828418, 'size': 1296}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 16163190
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16163212
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16163223
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 16163234
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 16163245
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 16163256
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 16163267
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16163278
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1], 'schur_index': 1}
  • id: 16163289
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 16163191
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 16163202
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, -2, 2, 2, 2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 16163204
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 16163205
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, -1, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, -1, -1, -1, 0, -1, -1, -1, -1, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16163206
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 2, 0, -2, 2, 0, -2, 0, 2, -2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -2, -2, 0, 2, 2, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, 0, 2, 2, 0, 0, 0, 2, 0, -2, -2, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 1, 2, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, -1, 1, 1, 0, 1, -1, -1, -1, -2, -2, -2, -2, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, -2, -2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 16163207
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 2, 0, -2, 2, 0, -2, 0, 2, -2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, -2, -2, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, 0, 2, 2, 0, 0, 0, 2, 0, -2, -2, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 1, 2, 2, 0, 0, 0, 0, -2, 0, -2, 0, 0, 2, 0, -1, 1, 1, 0, 1, -1, -1, -1, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, -2, -2, 0, 0, 2, 2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 16163208
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -2, -2, 0, -2, -2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, -1, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, -1, -1, -1, 0, -1, -1, -1, -1, -2, -2, -2, -2, 0, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, -2, -2, 0, 0, -2, -2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, 1], 'schur_index': 1}
  • id: 16163211
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, -1, 3, 1, 3, -1, 1, -1, 1, -1, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, -1, -1, -1, 1, 1, -1, 3, 3, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 3, -1, 1, 1, 1, 3, 1, 3, 3, 3, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 0, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 3, 3, 3, 3, -1, 3, 3, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 0, 1, 0, -1, -1, 1, 1, -1, 1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163213
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, 3, -1, 3, -1, -1, -1, -1, -1, 3, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 1, -1, -1, -1, -1, 1, 3, 3, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, -1, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 3, 3, 3, 3, 1, 3, 3, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, -1, 0, 1, 1, -1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163214
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, 3, -1, 3, -1, -1, -1, -1, -1, 3, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, -3, -3, 1, 1, 1, 1, 1, 1, -3, -3, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, -1, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, -3, -3, -3, -3, 1, -3, -3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163215
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, 3, 1, 3, -1, 1, -1, 1, -1, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, -3, -3, -1, 1, 1, -1, -1, -1, -3, -3, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 3, -1, 1, 1, 1, 3, 1, 3, 3, 3, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 0, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, -3, -3, -3, -3, -1, -3, -3, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 0, -1, 0, -1, -1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163216
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3e', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 1, 3, -1, -3, -1, 1, 1, -1, -1, -3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, -3, -3, -1, -1, -1, 1, 1, 1, 3, 3, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 3, -1, -1, -1, -1, 3, 1, -3, -3, 3, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 0, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, -3, -3, -3, -3, -1, -3, -3, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 0, 1, 0, 1, 1, 1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163217
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3f', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 1, 3, -1, -3, -1, 1, 1, -1, -1, -3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, -1, 1, 1, -1, -1, 1, -3, -3, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 3, -1, -1, -1, -1, 3, 1, -3, -3, 3, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 0, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 3, 3, 3, 3, -1, 3, 3, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 0, -1, 0, 1, 1, -1, 1, -1, 1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163218
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 1, 3, 1, -3, -1, -1, 1, 1, -1, -3, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, -3, -3, 1, -1, -1, -1, -1, -1, 3, 3, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 3, -1, 1, 1, 1, 3, -1, -3, -3, 3, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 0, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, -3, -3, -3, -3, 1, -3, -3, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, -1, 0, -1, -1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163219
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 1, 3, 1, -3, -1, -1, 1, 1, -1, -3, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 3, 3, 1, 1, 1, 1, 1, -1, -3, -3, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 3, -1, 1, 1, 1, 3, -1, -3, -3, 3, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 0, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 3, 3, 3, 3, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 0, 1, 0, -1, -1, 1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163209
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.2e', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 0, -4, 4, 0, 4, 0, -4, 4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, -4, -4, 0, -4, 4, 0, 0, 0, -4, 0, -4, -4, -4, 4, 4, 0, 0, 0, -4, -4, -4, -4, 0, 0, 2, 4, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, -4, 0, 2, 2, 2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 16163210
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.2f', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 4, 4, 0, -4, 0, -4, -4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 4, 0, -4, 4, 0, 0, 0, -4, 0, 4, 4, -4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, -2, 4, 4, 0, 0, 0, 0, -4, 0, -4, 0, 0, -4, 0, 2, -2, -2, 0, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 16163225
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4a', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, -2, 1, 4, 4, 4, -2, 1, -2, 1, -2, 1, 4, -2, 1, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, -2, 4, 4, 0, 4, -2, 1, 4, 0, 4, 1, -2, 0, 1, -2, -2, -2, 1, -2, 1, -2, 1, 1, -2, 4, -2, 1, 1, -2, 1, 0, 0, 0, 0, 1, -2, 0, 0, 0, -2, 1, 0, 0, 4, -2, 1, 0, 0, 0, 0, 4, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163226
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4b', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 1, -2, 4, 4, 4, 1, -2, 1, -2, 1, -2, 4, 1, -2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 4, 1, 4, 4, 0, 4, 1, -2, 4, 0, 4, -2, 1, 0, -2, 1, 1, 1, -2, 1, -2, 1, -2, -2, 1, 4, 1, -2, -2, 1, -2, 0, 0, 0, 0, -2, 1, 0, 0, 0, 1, -2, 0, 0, 4, 1, -2, 0, 0, 0, 0, 4, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163227
    {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4c', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, -4, -4, 4, 4, 0, 0, 0, 0, 0, -2, 1, 4, 4, 4, -2, 1, -2, 1, -2, 1, 4, -2, 1, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, -4, 2, -4, -4, 0, 4, 2, -1, -4, 0, 4, -1, 2, 0, 1, -2, 2, 2, -1, 2, -1, 2, -1, -1, -2, -4, -2, 1, 1, 2, -1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 2, -1, 0, 0, 4, -2, 1, 0, 0, 0, 0, 4, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163228
    {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4d', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, -4, -4, 4, 4, 0, 0, 0, 0, 0, 1, -2, 4, 4, 4, 1, -2, 1, -2, 1, -2, 4, 1, -2, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -4, -1, -4, -4, 0, 4, -1, 2, -4, 0, 4, 2, -1, 0, -2, 1, -1, -1, 2, -1, 2, -1, 2, 2, 1, -4, 1, -2, -2, -1, 2, 0, 0, 0, 0, -2, 1, 0, 0, 0, -1, 2, 0, 0, 4, 1, -2, 0, 0, 0, 0, 4, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163229
    {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4e', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 4, -4, 4, -4, 0, 0, 0, 0, 0, -2, 1, 4, 4, 4, -2, 1, -2, 1, -2, 1, 4, -2, 1, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -4, 2, -4, 4, 0, 4, -2, 1, 4, 0, -4, -1, 2, 0, 1, -2, -2, -2, 1, 2, -1, 2, -1, 1, 2, -4, -2, 1, -1, -2, 1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 2, -1, 0, 0, 4, -2, 1, 0, 0, 0, 0, -4, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163230
    {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4f', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 4, -4, 4, -4, 0, 0, 0, 0, 0, 1, -2, 4, 4, 4, 1, -2, 1, -2, 1, -2, 4, 1, -2, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, -4, -1, -4, 4, 0, 4, 1, -2, 4, 0, -4, 2, -1, 0, -2, 1, 1, 1, -2, -1, 2, -1, 2, -2, -1, -4, 1, -2, 2, 1, -2, 0, 0, 0, 0, 2, -1, 0, 0, 0, -1, 2, 0, 0, 4, 1, -2, 0, 0, 0, 0, -4, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163231
    {'cdim': 4, 'counter': 37, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4g', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, 4, 0, -4, 4, 4, -4, 0, 0, 0, 0, 0, -2, 1, 4, 4, 4, -2, 1, -2, 1, -2, 1, 4, -2, 1, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 4, -2, 4, -4, 0, 4, 2, -1, -4, 0, -4, 1, -2, 0, 1, -2, 2, 2, -1, -2, 1, -2, 1, -1, 2, 4, -2, 1, -1, 2, -1, 0, 0, 0, 0, -1, 2, 0, 0, 0, -2, 1, 0, 0, 4, -2, 1, 0, 0, 0, 0, -4, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163232
    {'cdim': 4, 'counter': 38, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.4h', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, 4, 0, -4, 4, 4, -4, 0, 0, 0, 0, 0, 1, -2, 4, 4, 4, 1, -2, 1, -2, 1, -2, 4, 1, -2, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 4, 1, 4, -4, 0, 4, -1, 2, -4, 0, -4, -2, 1, 0, -2, 1, -1, -1, 2, 1, -2, 1, -2, 2, -1, 4, 1, -2, 2, -1, 2, 0, 0, 0, 0, 2, -1, 0, 0, 0, 1, -2, 0, 0, 4, 1, -2, 0, 0, 0, 0, -4, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163220
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3i', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -2, -6, -2, 6, -2, -2, 2, 2, 2, -6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, -2, -2, -2, -2, -2, -6, -2, -2, -2, -2, -6, -2, 6, 6, -6, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163221
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3j', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -2, -6, 2, 6, -2, 2, 2, -2, 2, -6, -2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 2, -2, -2, -2, 2, -6, -2, 2, 2, 2, -6, 2, 6, 6, -6, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 0, -2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163222
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3k', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, 2, -6, -2, -6, -2, 2, -2, 2, 2, 6, -2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, -2, 2, 2, 2, -2, -6, -2, -2, -2, -2, -6, 2, -6, -6, -6, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 2, 0, -2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163224
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.3l', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, 2, -6, 2, -6, -2, -2, -2, -2, 2, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -6, -2, 2, 2, 2, -6, -2, -6, -6, -6, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163233
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6a', 'multiplicity': 1, 'nt': [9, 31], 'qdim': 6, 'qvalues': [6, 4, 6, 2, 0, 2, 0, 4, 2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, 6, 6, 2, 4, 4, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 1, 4, -2, -1, 3, -1, 2, 2, -1, -3, 0, 0, 0, 0, 2, 2, 2, -1, -1, 1, 1, -2, -2, 2, 0, 0, -1, -1, 0, -1, -1, 2, -2, -1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, -1, 0, 0, 2, 2, -1, 2, -1, -2, 1, 2, -2, 1, -1, -1, -1, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163235
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6b', 'multiplicity': 1, 'nt': [18, 300], 'qdim': 6, 'qvalues': [6, -4, 6, -2, 0, 2, 0, -4, -2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, 6, 6, 2, -4, -4, -2, -2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, -4, -2, -1, -4, 2, 1, 3, -1, -2, -2, 1, -3, 0, 0, 0, 0, 2, 2, -2, 1, 1, -1, -1, 2, 2, -2, 0, 0, -1, -1, 0, 1, 1, -2, 2, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, -1, 0, 0, 2, 2, 1, -2, 1, 2, -1, -2, 2, -1, -1, -1, -1, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163236
    {'cdim': 6, 'counter': 41, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6c', 'multiplicity': 1, 'nt': [18, 311], 'qdim': 6, 'qvalues': [6, -4, 6, 2, 0, 2, 0, -4, 2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, 6, 6, -2, -4, -4, 2, 2, 0, 0, 0, 2, 2, -2, -2, 0, 0, -2, 0, 0, 0, -4, 2, -1, -4, 2, -1, 3, -1, 2, 2, -1, -3, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 0, 0, -1, -1, 0, -1, -1, 2, 2, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, 1, 0, 0, -2, -2, -1, 2, -1, 2, -1, 2, 2, -1, 1, 1, -1, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163237
    {'cdim': 6, 'counter': 42, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6d', 'multiplicity': 1, 'nt': [18, 319], 'qdim': 6, 'qvalues': [6, 4, 6, -2, 0, 2, 0, 4, -2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, 6, 6, -2, 4, 4, -2, -2, 0, 0, 0, 2, 2, -2, -2, 0, 0, -2, 0, 0, 0, 4, -2, 1, 4, -2, 1, 3, -1, -2, -2, 1, -3, 0, 0, 0, 0, 2, 2, -2, 1, 1, 1, 1, -2, -2, -2, 0, 0, -1, -1, 0, 1, 1, -2, -2, 1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, 1, 0, 0, -2, -2, 1, -2, 1, -2, 1, -2, -2, 1, 1, 1, -1, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163238
    {'cdim': 6, 'counter': 43, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6e', 'multiplicity': 1, 'nt': [18, 394], 'qdim': 6, 'qvalues': [6, -4, 6, -2, 0, 2, 0, -4, -2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, -6, -6, 2, 4, 4, 2, 2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 0, 0, 0, -4, -2, -1, -4, 2, 1, 3, -1, -2, -2, 1, -3, 0, 0, 0, 0, 2, 2, -2, 1, 1, -1, -1, 2, 2, -2, 0, 0, -1, -1, 0, 1, 1, -2, 2, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, -1, 0, 0, 2, 2, -1, 2, -1, -2, 1, 2, -2, 1, -1, -1, 1, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163239
    {'cdim': 6, 'counter': 44, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6f', 'multiplicity': 1, 'nt': [18, 394], 'qdim': 6, 'qvalues': [6, -4, 6, 2, 0, 2, 0, -4, 2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, -6, -6, -2, 4, 4, -2, -2, 0, 0, 0, -2, -2, 2, 2, 0, 0, -2, 0, 0, 0, -4, 2, -1, -4, 2, -1, 3, -1, 2, 2, -1, -3, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 0, 0, -1, -1, 0, -1, -1, 2, 2, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, 1, 0, 0, -2, -2, 1, -2, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163240
    {'cdim': 6, 'counter': 45, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6g', 'multiplicity': 1, 'nt': [18, 394], 'qdim': 6, 'qvalues': [6, 4, 6, -2, 0, 2, 0, 4, -2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, -6, -6, -2, -4, -4, 2, 2, 0, 0, 0, -2, -2, 2, 2, 0, 0, -2, 0, 0, 0, 4, -2, 1, 4, -2, 1, 3, -1, -2, -2, 1, -3, 0, 0, 0, 0, 2, 2, -2, 1, 1, 1, 1, -2, -2, -2, 0, 0, -1, -1, 0, 1, 1, -2, -2, 1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, 1, 0, 0, -2, -2, -1, 2, -1, 2, -1, 2, 2, -1, 1, 1, 1, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163241
    {'cdim': 6, 'counter': 46, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6h', 'multiplicity': 1, 'nt': [18, 394], 'qdim': 6, 'qvalues': [6, 4, 6, 2, 0, 2, 0, 4, 2, 2, 0, 0, 6, 6, 3, -3, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, -6, -6, 2, -4, -4, -2, -2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 0, 0, 0, 4, 2, 1, 4, -2, -1, 3, -1, 2, 2, -1, -3, 0, 0, 0, 0, 2, 2, 2, -1, -1, 1, 1, -2, -2, 2, 0, 0, -1, -1, 0, -1, -1, 2, -2, -1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, -1, 0, 0, 2, 2, 1, -2, 1, 2, -1, -2, 2, -1, -1, -1, 1, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163247
    {'cdim': 8, 'counter': 51, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8a', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, -4, 2, 8, 8, 8, -4, 2, -4, 2, -4, 2, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 8, -4, 8, 0, 0, 8, 0, 0, 0, 0, 0, 2, -4, 0, 2, -4, 0, 0, 0, -4, 2, -4, 2, 0, 0, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163248
    {'cdim': 8, 'counter': 52, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8b', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 2, -4, 8, 8, 8, 2, -4, 2, -4, 2, -4, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 8, 2, 8, 0, 0, 8, 0, 0, 0, 0, 0, -4, 2, 0, -4, 2, 0, 0, 0, 2, -4, 2, -4, 0, 0, -4, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163249
    {'cdim': 8, 'counter': 53, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8c', 'multiplicity': 1, 'nt': [12, 213], 'qdim': 8, 'qvalues': [8, 0, 8, 4, 0, 0, 0, 0, 4, 0, 0, 0, 8, 8, -4, -1, 2, -4, -4, -1, -1, 2, 2, 2, 2, 2, 8, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -4, 0, 4, 4, 1, -1, 0, 0, 0, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, -2, 0, -2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, -1, -1, -1, -4, -4, -1, -1, 0, 2, 2, 0, 0, -2, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 16163250
    {'cdim': 8, 'counter': 54, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8d', 'multiplicity': 1, 'nt': [24, 1310], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, -4, 2, 8, 8, 8, -4, 2, -4, 2, -4, 2, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -8, 4, -8, 0, 0, 8, 0, 0, 0, 0, 0, -2, 4, 0, 2, -4, 0, 0, 0, 4, -2, 4, -2, 0, 0, 4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163251
    {'cdim': 8, 'counter': 55, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8e', 'multiplicity': 1, 'nt': [24, 1310], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 2, -4, 8, 8, 8, 2, -4, 2, -4, 2, -4, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -8, -2, -8, 0, 0, 8, 0, 0, 0, 0, 0, 4, -2, 0, -4, 2, 0, 0, 0, -2, 4, -2, 4, 0, 0, 4, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163252
    {'cdim': 8, 'counter': 56, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8f', 'multiplicity': 1, 'nt': [24, 2893], 'qdim': 8, 'qvalues': [8, 0, 8, -4, 0, 0, 0, 0, -4, 0, 0, 0, 8, 8, -4, -1, 2, -4, -4, -1, -1, 2, 2, 2, 2, 2, 8, 8, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -4, 0, -4, -4, -1, -1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, 2, 0, 2, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, -1, -1, -4, -4, -1, -1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, -1, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 16163253
    {'cdim': 8, 'counter': 57, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8g', 'multiplicity': 1, 'nt': [24, 5223], 'qdim': 8, 'qvalues': [8, 0, 8, -4, 0, 0, 0, 0, -4, 0, 0, 0, 8, 8, -4, -1, 2, -4, -4, -1, -1, 2, 2, 2, 2, 2, -8, -8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -4, 0, -4, -4, -1, -1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, 2, 0, 2, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, -1, -1, 4, 4, 1, 1, 0, -2, -2, 0, 0, -2, -2, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 1, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
  • id: 16163254
    {'cdim': 8, 'counter': 58, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8h', 'multiplicity': 1, 'nt': [24, 5223], 'qdim': 8, 'qvalues': [8, 0, 8, 4, 0, 0, 0, 0, 4, 0, 0, 0, 8, 8, -4, -1, 2, -4, -4, -1, -1, 2, 2, 2, 2, 2, -8, -8, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, -4, 0, 4, 4, 1, -1, 0, 0, 0, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, -2, 0, -2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, -1, -1, -1, 4, 4, 1, 1, 0, -2, -2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -1, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
  • id: 16163242
    {'cdim': 6, 'counter': 47, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6i', 'multiplicity': 2, 'nt': [36, 6146], 'qdim': 12, 'qvalues': [12, -8, -12, -4, 0, 4, 0, 8, 4, -4, 0, 0, 12, 12, 6, -6, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -8, -4, -2, -8, 4, 2, -6, -2, -4, -4, 2, 6, 0, 0, 0, 0, 4, 4, -4, 2, 2, -2, -2, 4, 4, -4, 0, 0, -2, -2, 0, 2, 2, 4, -4, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163243
    {'cdim': 6, 'counter': 48, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6j', 'multiplicity': 2, 'nt': [36, 6146], 'qdim': 12, 'qvalues': [12, -8, -12, 4, 0, 4, 0, 8, -4, -4, 0, 0, 12, 12, 6, -6, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 4, -2, -8, 4, -2, -6, -2, 4, 4, -2, 6, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, 4, 4, 4, 0, 0, -2, -2, 0, -2, -2, -4, -4, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163244
    {'cdim': 6, 'counter': 49, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6k', 'multiplicity': 2, 'nt': [36, 6146], 'qdim': 12, 'qvalues': [12, 8, -12, -4, 0, 4, 0, -8, 4, -4, 0, 0, 12, 12, 6, -6, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, -4, 2, 8, -4, 2, -6, -2, -4, -4, 2, 6, 0, 0, 0, 0, 4, 4, -4, 2, 2, 2, 2, -4, -4, -4, 0, 0, -2, -2, 0, 2, 2, 4, 4, -2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163246
    {'cdim': 6, 'counter': 50, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.6l', 'multiplicity': 2, 'nt': [36, 6146], 'qdim': 12, 'qvalues': [12, 8, -12, 4, 0, 4, 0, -8, -4, -4, 0, 0, 12, 12, 6, -6, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 8, 4, 2, 8, -4, -2, -6, -2, 4, 4, -2, 6, 0, 0, 0, 0, 4, 4, 4, -2, -2, 2, 2, -4, -4, 4, 0, 0, -2, -2, 0, -2, -2, -4, 4, 2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163258
    {'cdim': 12, 'counter': 61, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12a', 'multiplicity': 1, 'nt': [18, 315], 'qdim': 12, 'qvalues': [12, 4, 12, 2, 0, 0, 2, 4, 2, 0, 0, 2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, 12, 12, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, -1, -2, 4, 1, 2, 0, 0, 2, 2, -1, 3, -1, 0, 0, -3, 0, 0, -1, 2, 2, -2, -2, 1, 1, -1, 2, 0, 0, 0, 2, -1, -1, -1, 1, 2, -2, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 3, 0, -3, -3, 0, 0, 2, -1, 2, 1, -2, -1, 1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163259
    {'cdim': 12, 'counter': 62, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12b', 'multiplicity': 1, 'nt': [24, 2659], 'qdim': 12, 'qvalues': [12, -4, 0, 4, 12, -4, 4, 0, 0, 0, 0, 0, -6, 3, 12, 12, 12, -6, 3, -6, 3, -6, 3, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -4, 2, -4, 4, 0, -4, -2, 1, 4, 0, 4, 3, -6, 0, -1, 2, -2, -2, 1, 2, -1, 2, -1, 1, -2, 0, 2, -1, 1, -2, 1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163260
    {'cdim': 12, 'counter': 63, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12c', 'multiplicity': 1, 'nt': [24, 2659], 'qdim': 12, 'qvalues': [12, -4, 0, 4, 12, -4, 4, 0, 0, 0, 0, 0, 3, -6, 12, 12, 12, 3, -6, 3, -6, 3, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, -4, -1, -4, 4, 0, -4, 1, -2, 4, 0, 4, -6, 3, 0, 2, -1, 1, 1, -2, -1, 2, -1, 2, -2, 1, 0, -1, 2, -2, 1, -2, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163261
    {'cdim': 12, 'counter': 64, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12d', 'multiplicity': 1, 'nt': [36, 1357], 'qdim': 12, 'qvalues': [12, -4, 0, -4, 12, -4, -4, 0, 0, 0, 0, 0, -6, 3, 12, 12, 12, -6, 3, -6, 3, -6, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, -4, 2, -4, -4, 0, -4, 2, -1, -4, 0, -4, 3, -6, 0, -1, 2, 2, 2, -1, 2, -1, 2, -1, -1, 2, 0, 2, -1, -1, 2, -1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163262
    {'cdim': 12, 'counter': 65, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12e', 'multiplicity': 1, 'nt': [36, 1357], 'qdim': 12, 'qvalues': [12, -4, 0, -4, 12, -4, -4, 0, 0, 0, 0, 0, 3, -6, 12, 12, 12, 3, -6, 3, -6, 3, -6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -4, -1, -4, -4, 0, -4, -1, 2, -4, 0, -4, -6, 3, 0, 2, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, 0, -1, 2, 2, -1, 2, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163263
    {'cdim': 12, 'counter': 66, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12f', 'multiplicity': 1, 'nt': [36, 2210], 'qdim': 12, 'qvalues': [12, 0, 12, 0, 0, -4, 0, 0, 0, -4, 0, 0, 12, 12, 6, -6, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, -6, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163264
    {'cdim': 12, 'counter': 67, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12g', 'multiplicity': 1, 'nt': [36, 2214], 'qdim': 12, 'qvalues': [12, -4, 12, 2, 0, 0, -2, -4, 2, 0, 0, -2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, 12, 12, 0, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -4, -1, 2, -4, -1, 2, 0, 0, 2, 2, -1, 3, 1, 0, 0, -3, 0, 0, -1, 2, 2, 2, 2, -1, -1, -1, -2, 0, 0, 0, -2, -1, -1, -1, -1, 2, 2, 1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 3, 0, -3, -3, 0, 0, 2, -1, 2, -1, 2, -1, -1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163265
    {'cdim': 12, 'counter': 68, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12h', 'multiplicity': 1, 'nt': [36, 2216], 'qdim': 12, 'qvalues': [12, 4, 12, -2, 0, 0, -2, 4, -2, 0, 0, -2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, 12, 12, 0, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 4, 1, -2, 4, 1, -2, 0, 0, -2, -2, 1, 3, 1, 0, 0, -3, 0, 0, 1, -2, -2, -2, -2, 1, 1, 1, -2, 0, 0, 0, -2, 1, 1, 1, 1, -2, -2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 3, 0, -3, -3, 0, 0, -2, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163266
    {'cdim': 12, 'counter': 69, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12i', 'multiplicity': 1, 'nt': [36, 2217], 'qdim': 12, 'qvalues': [12, -4, 12, -2, 0, 0, 2, -4, -2, 0, 0, 2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, 12, 12, 0, -4, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -4, 1, 2, -4, -1, -2, 0, 0, -2, -2, 1, 3, -1, 0, 0, -3, 0, 0, 1, -2, -2, 2, 2, -1, -1, 1, 2, 0, 0, 0, 2, 1, 1, 1, -1, -2, 2, -1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3, 3, 0, -3, -3, 0, 0, -2, 1, -2, -1, 2, 1, -1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163268
    {'cdim': 12, 'counter': 70, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12j', 'multiplicity': 1, 'nt': [36, 2459], 'qdim': 12, 'qvalues': [12, 4, 0, -4, -12, -4, 4, 0, 0, 0, 0, 0, -6, 3, 12, 12, 12, -6, 3, -6, 3, -6, 3, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 4, -2, 4, -4, 0, -4, 2, -1, -4, 0, 4, -3, 6, 0, -1, 2, 2, 2, -1, -2, 1, -2, 1, -1, -2, 0, 2, -1, 1, 2, -1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163269
    {'cdim': 12, 'counter': 71, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12k', 'multiplicity': 1, 'nt': [36, 2459], 'qdim': 12, 'qvalues': [12, 4, 0, -4, -12, -4, 4, 0, 0, 0, 0, 0, 3, -6, 12, 12, 12, 3, -6, 3, -6, 3, -6, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 4, 1, 4, -4, 0, -4, -1, 2, -4, 0, 4, 6, -3, 0, 2, -1, -1, -1, 2, 1, -2, 1, -2, 2, 1, 0, -1, 2, -2, -1, 2, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163270
    {'cdim': 12, 'counter': 72, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12l', 'multiplicity': 1, 'nt': [36, 2459], 'qdim': 12, 'qvalues': [12, 4, 0, 4, -12, -4, -4, 0, 0, 0, 0, 0, -6, 3, 12, 12, 12, -6, 3, -6, 3, -6, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 4, -2, 4, 4, 0, -4, -2, 1, 4, 0, -4, -3, 6, 0, -1, 2, -2, -2, 1, -2, 1, -2, 1, 1, 2, 0, 2, -1, -1, -2, 1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163271
    {'cdim': 12, 'counter': 73, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12m', 'multiplicity': 1, 'nt': [36, 2459], 'qdim': 12, 'qvalues': [12, 4, 0, 4, -12, -4, -4, 0, 0, 0, 0, 0, 3, -6, 12, 12, 12, 3, -6, 3, -6, 3, -6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 4, 1, 4, 4, 0, -4, 1, -2, 4, 0, -4, 6, -3, 0, 2, -1, 1, 1, -2, 1, -2, 1, -2, -2, -1, 0, -1, 2, 2, 1, -2, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163272
    {'cdim': 12, 'counter': 74, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12n', 'multiplicity': 1, 'nt': [36, 3831], 'qdim': 12, 'qvalues': [12, 0, 12, 0, 0, -4, 0, 0, 0, -4, 0, 0, 12, 12, 6, -6, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, -6, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163273
    {'cdim': 12, 'counter': 75, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12o', 'multiplicity': 1, 'nt': [36, 3850], 'qdim': 12, 'qvalues': [12, -4, 12, -2, 0, 0, 2, -4, -2, 0, 0, 2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, -12, -12, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -4, 1, 2, -4, -1, -2, 0, 0, -2, -2, 1, 3, -1, 0, 0, -3, 0, 0, 1, -2, -2, 2, 2, -1, -1, 1, 2, 0, 0, 0, 2, 1, 1, 1, -1, -2, 2, -1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, 2, -1, 2, 1, -2, -1, 1, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163274
    {'cdim': 12, 'counter': 76, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12p', 'multiplicity': 1, 'nt': [36, 3850], 'qdim': 12, 'qvalues': [12, -4, 12, 2, 0, 0, -2, -4, 2, 0, 0, -2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, -12, -12, 0, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -4, -1, 2, -4, -1, 2, 0, 0, 2, 2, -1, 3, 1, 0, 0, -3, 0, 0, -1, 2, 2, 2, 2, -1, -1, -1, -2, 0, 0, 0, -2, -1, -1, -1, -1, 2, 2, 1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, -2, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163275
    {'cdim': 12, 'counter': 77, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12q', 'multiplicity': 1, 'nt': [36, 3850], 'qdim': 12, 'qvalues': [12, 4, 12, -2, 0, 0, -2, 4, -2, 0, 0, -2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, -12, -12, 0, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 1, -2, 4, 1, -2, 0, 0, -2, -2, 1, 3, 1, 0, 0, -3, 0, 0, 1, -2, -2, -2, -2, 1, 1, 1, -2, 0, 0, 0, -2, 1, 1, 1, 1, -2, -2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, 2, -1, 2, -1, 2, -1, -1, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163276
    {'cdim': 12, 'counter': 78, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12r', 'multiplicity': 1, 'nt': [36, 3850], 'qdim': 12, 'qvalues': [12, 4, 12, 2, 0, 0, 2, 4, 2, 0, 0, 2, 12, 12, 0, 3, -3, 0, 0, 3, 3, -3, -3, 0, 0, 0, -12, -12, 0, -4, -4, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 4, -1, -2, 4, 1, 2, 0, 0, 2, 2, -1, 3, -1, 0, 0, -3, 0, 0, -1, 2, 2, -2, -2, 1, 1, -1, 2, 0, 0, 0, 2, -1, -1, -1, 1, 2, -2, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, -2, 1, -2, -1, 2, 1, -1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163255
    {'cdim': 8, 'counter': 59, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8i', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -16, -8, 0, 0, 0, 0, 8, 0, 0, 0, 16, 16, -8, -2, 4, -8, -8, -2, -2, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 8, 0, -8, -8, -2, 2, 0, 0, 0, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, -2, -4, 0, -4, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 16163257
    {'cdim': 8, 'counter': 60, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.8j', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -16, 8, 0, 0, 0, 0, -8, 0, 0, 0, 16, 16, -8, -2, 4, -8, -8, -2, -2, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 8, 0, 8, 8, 2, 2, 0, 0, 0, -4, 0, 0, -4, -4, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 2, 4, 0, 4, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], 'schur_index': 1}
  • id: 16163283
    {'cdim': 16, 'counter': 84, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.16a', 'multiplicity': 1, 'nt': [24, 2912], 'qdim': 16, 'qvalues': [16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, -8, -2, 4, -8, -8, -2, -2, 4, 4, -2, -2, -2, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 1, -8, -8, -2, -2, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
  • id: 16163284
    {'cdim': 16, 'counter': 85, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.16b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, -8, -2, 4, -8, -8, -2, -2, 4, 4, -2, -2, -2, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 1, 8, 8, 2, 2, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1], 'schur_index': 1}
  • id: 16163277
    {'cdim': 12, 'counter': 79, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12s', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -24, -4, 0, 0, 4, 8, 4, 0, 0, -4, 24, 24, 0, 6, -6, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 2, 4, -8, -2, -4, 0, 0, -4, -4, 2, -6, -2, 0, 0, 6, 0, 0, 2, -4, -4, 4, 4, -2, -2, 2, 4, 0, 0, 0, 4, 2, 2, -2, 2, 4, -4, -2, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163279
    {'cdim': 12, 'counter': 80, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12t', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -24, 4, 0, 0, -4, 8, -4, 0, 0, 4, 24, 24, 0, 6, -6, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -2, 4, -8, -2, 4, 0, 0, 4, 4, -2, -6, 2, 0, 0, 6, 0, 0, -2, 4, 4, 4, 4, -2, -2, -2, -4, 0, 0, 0, -4, -2, -2, 2, 2, -4, -4, 2, 2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163280
    {'cdim': 12, 'counter': 81, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12u', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 0, -24, 0, 0, -8, 0, 0, 0, 8, 0, 0, 24, 24, 12, -12, 0, 12, 12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 4, 0, 0, 0, 12, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163281
    {'cdim': 12, 'counter': 82, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12v', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 8, -24, -4, 0, 0, -4, -8, 4, 0, 0, 4, 24, 24, 0, 6, -6, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, -4, 8, 2, -4, 0, 0, -4, -4, 2, -6, 2, 0, 0, 6, 0, 0, 2, -4, -4, -4, -4, 2, 2, 2, -4, 0, 0, 0, -4, 2, 2, -2, -2, 4, 4, 2, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163282
    {'cdim': 12, 'counter': 83, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.12w', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 8, -24, 4, 0, 0, 4, -8, -4, 0, 0, -4, 24, 24, 0, 6, -6, 0, 0, 6, 6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -2, -4, 8, 2, 4, 0, 0, 4, 4, -2, -6, -2, 0, 0, 6, 0, 0, -2, 4, 4, -4, -4, 2, 2, -2, 4, 0, 0, 0, 4, -2, -2, 2, -2, -4, 4, -2, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163286
    {'cdim': 24, 'counter': 87, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24a', 'multiplicity': 1, 'nt': [36, 16101], 'qdim': 24, 'qvalues': [24, 16, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, -12, 6, 12, -12, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 4, -8, -8, -4, 0, -4, -4, 2, -4, 0, 0, 0, 0, 0, 2, -4, -4, 2, -1, -2, 1, 4, -2, 2, 0, 0, 2, -1, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163287
    {'cdim': 24, 'counter': 88, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24b', 'multiplicity': 1, 'nt': [36, 16101], 'qdim': 24, 'qvalues': [24, 16, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 6, -12, 12, -12, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 4, 4, -8, -4, 0, -4, 2, -4, -4, 0, 0, 0, 0, 0, -4, 2, 2, -1, 2, 1, -2, -2, 4, -4, 0, 0, -1, 2, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163288
    {'cdim': 24, 'counter': 89, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -16, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, -12, 6, 12, -12, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -8, -4, 8, 8, 4, 0, -4, 4, -2, 4, 0, 0, 0, 0, 0, 2, -4, 4, -2, 1, 2, -1, -4, 2, -2, 0, 0, 2, -1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163290
    {'cdim': 24, 'counter': 90, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -16, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 6, -12, 12, -12, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, -4, -4, 8, 4, 0, -4, -2, 4, 4, 0, 0, 0, 0, 0, -4, 2, -2, 1, -2, -1, 2, 2, -4, 4, 0, 0, -1, 2, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163291
    {'cdim': 24, 'counter': 91, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24e', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -16, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, -12, 6, 12, -12, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, 8, 8, -4, 0, -4, -4, 2, -4, 0, 0, 0, 0, 0, 2, -4, -4, 2, -1, 2, -1, -4, 2, 2, 0, 0, 2, -1, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163292
    {'cdim': 24, 'counter': 92, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24f', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -16, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 6, -12, 12, -12, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, -4, -4, 8, -4, 0, -4, 2, -4, -4, 0, 0, 0, 0, 0, -4, 2, 2, -1, 2, -1, 2, 2, -4, -4, 0, 0, -1, 2, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163293
    {'cdim': 24, 'counter': 93, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24g', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 16, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, -12, 6, 12, -12, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, 4, -8, -8, 4, 0, -4, 4, -2, 4, 0, 0, 0, 0, 0, 2, -4, 4, -2, 1, -2, 1, 4, -2, -2, 0, 0, 2, -1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163294
    {'cdim': 24, 'counter': 94, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.24h', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 16, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 6, -12, 12, -12, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 4, 4, -8, 4, 0, -4, -2, 4, 4, 0, 0, 0, 0, 0, -4, 2, -2, 1, -2, 1, -2, -2, 4, 4, 0, 0, -1, 2, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163285
    {'cdim': 16, 'counter': 86, 'faithful': False, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.16c', 'multiplicity': 2, 'nt': [96, 0], 'qdim': 32, 'qvalues': [32, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 32, -16, -4, 8, -16, -16, -4, -4, 8, 8, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
  • id: 16163295
    {'cdim': 32, 'counter': 95, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.32a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, -16, 8, -16, -4, 8, 8, -4, 2, -1, -4, 2, 8, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163296
    {'cdim': 32, 'counter': 96, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.32b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 8, -16, -16, -4, 8, -4, 8, -1, 2, 2, -4, 8, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 4, -8, 4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163297
    {'cdim': 32, 'counter': 97, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.32c', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 32, 'qvalues': [32, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -16, 8, -16, -4, 8, 8, -4, 2, -1, -4, 2, 8, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163298
    {'cdim': 32, 'counter': 98, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.32d', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 32, 'qvalues': [32, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 8, -16, -16, -4, 8, -4, 8, -1, 2, 2, -4, 8, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163299
    {'cdim': 48, 'counter': 99, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48a', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, -24, 12, 0, 12, -12, 0, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -8, -8, 4, 8, 0, 0, -4, 2, -4, 0, -4, 0, 0, 0, 0, 0, 2, -4, 2, 4, -2, -2, 1, -1, -4, 0, 0, 0, 2, 2, -1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163192
    {'cdim': 48, 'counter': 100, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 12, -24, 0, 12, -12, 0, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -4, -8, 4, 4, 8, 0, 0, 2, -4, -4, 0, -4, 0, 0, 0, 0, 0, -1, 2, -4, -2, 4, 1, -2, 2, 2, 0, 0, 0, -4, -1, 2, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163193
    {'cdim': 48, 'counter': 101, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48c', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -16, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -24, 12, 0, 12, -12, 0, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 8, 8, -4, -8, 0, 0, 4, -2, 4, 0, -4, 0, 0, 0, 0, 0, -2, 4, -2, -4, 2, 2, -1, 1, -4, 0, 0, 0, 2, -2, 1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163194
    {'cdim': 48, 'counter': 102, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48d', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -16, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 12, -24, 0, 12, -12, 0, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 8, -4, -4, -8, 0, 0, -2, 4, 4, 0, -4, 0, 0, 0, 0, 0, 1, -2, 4, 2, -4, -1, 2, -2, 2, 0, 0, 0, -4, 1, -2, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163195
    {'cdim': 48, 'counter': 103, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48e', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -24, 12, 0, 12, -12, 0, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 8, 8, -4, 8, 0, 0, -4, 2, -4, 0, 4, 0, 0, 0, 0, 0, 2, -4, 2, -4, 2, 2, -1, -1, 4, 0, 0, 0, -2, 2, -1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163196
    {'cdim': 48, 'counter': 104, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48f', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 12, -24, 0, 12, -12, 0, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, 8, -4, -4, 8, 0, 0, 2, -4, -4, 0, 4, 0, 0, 0, 0, 0, -1, 2, -4, 2, -4, -1, 2, 2, -2, 0, 0, 0, 4, -1, 2, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163197
    {'cdim': 48, 'counter': 105, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48g', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -24, 12, 24, -24, 0, -12, 6, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163198
    {'cdim': 48, 'counter': 106, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48h', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 12, -24, 24, -24, 0, 6, -12, -6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163199
    {'cdim': 48, 'counter': 107, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48i', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, -24, 12, 0, 12, -12, 0, 0, -6, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -8, -8, 4, -8, 0, 0, 4, -2, 4, 0, 4, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, -2, 1, 1, 4, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163200
    {'cdim': 48, 'counter': 108, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.48j', 'multiplicity': 1, 'nt': [144, 0], 'qdim': 48, 'qvalues': [48, 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 12, -24, 0, 12, -12, 0, 0, 3, -6, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, -8, 4, 4, -8, 0, 0, -2, 4, 4, 0, 4, 0, 0, 0, 0, 0, 1, -2, 4, -2, 4, 1, -2, -2, -2, 0, 0, 0, 4, 1, -2, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163201
    {'cdim': 64, 'counter': 109, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.64a', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 64, 'qvalues': [64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 16, -32, -8, 16, 16, -8, 4, -2, -8, 4, -8, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16163203
    {'cdim': 64, 'counter': 110, 'faithful': True, 'group': '46656.ir', 'group_order': 46656, 'image': None, 'label': '46656.ir.64b', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 64, 'qvalues': [64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -32, -32, -8, 16, -8, 16, -2, 4, 4, -8, -8, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

  Column	Type
  center	text
  center_index	numeric
  center_order	numeric
  counter	smallint
  cyclotomic_n	integer
  dim	integer
  faithful	boolean
  field	numeric[]
  group	text
  group_counter	integer
  group_order	numeric
  image	text
  image_isoclass	text
  image_order	numeric
  indicator	smallint
  kernel	text
  kernel_order	numeric
  label	text
  nt	integer[]
  q_character	text
  values	jsonb

  
  
  • id: 36249191
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 46656, 'label': '46656.ir.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36249235
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 23328, 'label': '46656.ir.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36249246
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 23328, 'label': '46656.ir.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36249257
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 23328, 'label': '46656.ir.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36249268
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 23328, 'label': '46656.ir.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36249279
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 23328, 'label': '46656.ir.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36249290
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 23328, 'label': '46656.ir.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36249301
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 23328, 'label': '46656.ir.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36249312
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  • id: 36249192
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.k1', 'kernel_order': 11664, 'label': '46656.ir.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 36249203
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.j1', 'kernel_order': 11664, 'label': '46656.ir.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 36249214
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.j1', 'kernel_order': 11664, 'label': '46656.ir.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 36249225
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1', 'kernel_order': 11664, 'label': '46656.ir.1k1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 36249229
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1', 'kernel_order': 11664, 'label': '46656.ir.1k2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 36249230
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 11664, 'label': '46656.ir.1l1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 36249231
    {'center': '1.a1', 'center_index': 1, 'center_order': 46656, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 11664, 'label': '46656.ir.1l2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 36249232
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  • id: 36249233
    {'center': '6.a1', 'center_index': 6, 'center_order': 7776, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 3888, 'label': '46656.ir.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36249234
    {'center': '6.a1', 'center_index': 6, 'center_order': 7776, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 3888, 'label': '46656.ir.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36249236
    {'center': '6.a1', 'center_index': 6, 'center_order': 7776, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 3888, 'label': '46656.ir.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36249237
    {'center': '6.a1', 'center_index': 6, 'center_order': 7776, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1', 'kernel_order': 1944, 'label': '46656.ir.2e1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 36249238
    {'center': '6.a1', 'center_index': 6, 'center_order': 7776, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.d1', 'kernel_order': 1944, 'label': '46656.ir.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 36249239
    {'center': '6.a1', 'center_index': 6, 'center_order': 7776, 'counter': 23, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 1944, 'label': '46656.ir.2f1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 36249240
    {'center': '6.a1', 'center_index': 6, 'center_order': 7776, 'counter': 24, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 1944, 'label': '46656.ir.2f2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 36249241
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  • id: 36249242
    {'center': '24.b1', 'center_index': 24, 'center_order': 1944, 'counter': 26, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1', 'kernel_order': 1944, 'label': '46656.ir.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249243
    {'center': '24.b1', 'center_index': 24, 'center_order': 1944, 'counter': 27, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 972, 'label': '46656.ir.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249244
    {'center': '24.b1', 'center_index': 24, 'center_order': 1944, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 972, 'label': '46656.ir.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249245
    {'center': '24.b1', 'center_index': 24, 'center_order': 1944, 'counter': 29, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1', 'kernel_order': 972, 'label': '46656.ir.3e', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249247
    {'center': '24.b1', 'center_index': 24, 'center_order': 1944, 'counter': 30, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 972, 'label': '46656.ir.3f', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249248
    {'center': '24.b1', 'center_index': 24, 'center_order': 1944, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1', 'kernel_order': 972, 'label': '46656.ir.3g', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249249
    {'center': '24.b1', 'center_index': 24, 'center_order': 1944, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 972, 'label': '46656.ir.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249250
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  • id: 36249251
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  • id: 36249252
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  • id: 36249253
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  • id: 36249254
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  • id: 36249255
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  • id: 36249256
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  • id: 36249258
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  • id: 36249259
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  • id: 36249260
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  • id: 36249261
    {'center': '36.a1', 'center_index': 36, 'center_order': 1296, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '72.45', 'image_order': 72, 'indicator': 1, 'kernel': '72.c1', 'kernel_order': 648, 'label': '46656.ir.4c', 'nt': [12, 40], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249262
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  • id: 36249263
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  • id: 36249264
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  • id: 36249265
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  • id: 36249266
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  • id: 36249267
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  • id: 36249269
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  • id: 36249270
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  • id: 36249271
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  • id: 36249272
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  • id: 36249273
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  • id: 36249274
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  • id: 36249275
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  • id: 36249276
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  • id: 36249277
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  • id: 36249278
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  • id: 36249280
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  • id: 36249281
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  • id: 36249282
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  • id: 36249283
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  • id: 36249284
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  • id: 36249285
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  • id: 36249286
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  • id: 36249287
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  • id: 36249288
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  • id: 36249289
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  • id: 36249291
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  • id: 36249292
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  • id: 36249293
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  • id: 36249294
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  • id: 36249295
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  • id: 36249296
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  • id: 36249297
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  • id: 36249298
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  • id: 36249299
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  • id: 36249300
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  • id: 36249302
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  • id: 36249303
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  • id: 36249304
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 82, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 36, 'label': '46656.ir.12f', 'nt': [36, 2210], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249305
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 83, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 36, 'label': '46656.ir.12g', 'nt': [36, 2214], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249306
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 84, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 36, 'label': '46656.ir.12h', 'nt': [36, 2216], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249307
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 85, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1296.3490', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 36, 'label': '46656.ir.12i', 'nt': [36, 2217], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249308
    {'center': '864.a1', 'center_index': 864, 'center_order': 54, 'counter': 86, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1728.47869', 'image_order': 1728, 'indicator': 1, 'kernel': '1728.a1', 'kernel_order': 27, 'label': '46656.ir.12j', 'nt': [36, 2459], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249309
    {'center': '864.a1', 'center_index': 864, 'center_order': 54, 'counter': 87, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1728.47869', 'image_order': 1728, 'indicator': 1, 'kernel': '1728.a1', 'kernel_order': 27, 'label': '46656.ir.12k', 'nt': [36, 2459], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249310
    {'center': '864.a1', 'center_index': 864, 'center_order': 54, 'counter': 88, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '1728.47869', 'image_order': 1728, 'indicator': 1, 'kernel': '1728.a1', 'kernel_order': 27, 'label': '46656.ir.12l', 'nt': [36, 2459], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[-12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[12, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249311
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  • id: 36249313
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 90, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2592.cg', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 18, 'label': '46656.ir.12n', 'nt': [36, 3831], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249314
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 91, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2592.cg', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 18, 'label': '46656.ir.12o', 'nt': [36, 3850], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249315
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 92, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2592.cg', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 18, 'label': '46656.ir.12p', 'nt': [36, 3850], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[12, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249316
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 93, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2592.cg', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 18, 'label': '46656.ir.12q', 'nt': [36, 3850], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249317
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 94, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '2592.cg', 'image_order': 2592, 'indicator': 1, 'kernel': '2592.a1', 'kernel_order': 18, 'label': '46656.ir.12r', 'nt': [36, 3850], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[12, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249318
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 95, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12s1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 1]], [[12, 1]], [[0, 0]], [[4, 1]], [[-4, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-1, 1]], [[-2, 1]], [[1, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249319
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 96, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12s2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[-12, 1]], [[0, 0]], [[-4, 1]], [[4, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[1, 1]], [[2, 1]], [[-1, 1]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249320
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  • id: 36249321
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 98, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12t2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-12, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[-12, 1]], [[0, 0]], [[-4, 1]], [[4, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-1, 1]], [[-2, 1]], [[-1, 1]], [[-2, 1]], [[1, 1]], [[1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249322
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 99, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12u1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[-6, 1]], [[-6, 1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249193
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 100, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12u2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[-12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[6, 1]], [[6, 1]], [[-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249194
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 101, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12v1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 1]], [[12, 1]], [[0, 0]], [[-4, 1]], [[4, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-1, 1]], [[-2, 1]], [[-1, 1]], [[-2, 1]], [[1, 1]], [[1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249195
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 102, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12v2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-12, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[-12, 1]], [[0, 0]], [[4, 1]], [[-4, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[1, 1]], [[2, 1]], [[1, 1]], [[2, 1]], [[-1, 1]], [[-1, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249196
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 103, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12w1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-12, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 1]], [[12, 1]], [[0, 0]], [[-4, 1]], [[4, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[1, 1]], [[2, 1]], [[-1, 1]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249197
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 104, 'cyclotomic_n': 4, 'dim': 12, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.12w2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-12, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[-12, 1]], [[0, 0]], [[4, 1]], [[-4, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-1, 1]], [[-2, 1]], [[1, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249198
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  • id: 36249199
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  • id: 36249200
    {'center': '1296.a1', 'center_index': 1296, 'center_order': 36, 'counter': 107, 'cyclotomic_n': 4, 'dim': 16, 'faithful': False, 'field': [1, 0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '5184.og', 'image_order': 5184, 'indicator': 0, 'kernel': '5184.a1', 'kernel_order': 9, 'label': '46656.ir.16c1', 'nt': [96, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-16, 1]], [[16, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-8, 1]], [[8, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 36249201
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  • id: 36249202
    {'center': '46656.a1', 'center_index': 46656, 'center_order': 1, 'counter': 109, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ir', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1', 'kernel_order': 1, 'label': '46656.ir.24a', 'nt': [36, 16101], 'q_character': None, 'values': [[[24, 0]], [[16, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[6, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[8, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249204
    {'center': '46656.a1', 'center_index': 46656, 'center_order': 1, 'counter': 110, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ir', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1', 'kernel_order': 1, 'label': '46656.ir.24b', 'nt': [36, 16101], 'q_character': None, 'values': [[[24, 0]], [[16, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249205
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  • id: 36249206
    {'center': '46656.a1', 'center_index': 46656, 'center_order': 1, 'counter': 112, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ir', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1', 'kernel_order': 1, 'label': '46656.ir.24d', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[-16, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249207
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  • id: 36249208
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  • id: 36249209
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  • id: 36249210
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  • id: 36249211
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  • id: 36249212
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  • id: 36249213
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  • id: 36249215
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  • id: 36249216
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  • id: 36249217
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  • id: 36249218
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  • id: 36249219
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  • id: 36249220
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  • id: 36249221
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  • id: 36249222
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  • id: 36249223
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  • id: 36249224
    {'center': '46656.a1', 'center_index': 46656, 'center_order': 1, 'counter': 129, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ir', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1', 'kernel_order': 1, 'label': '46656.ir.48i', 'nt': [144, 0], 'q_character': None, 'values': [[[48, 0]], [[16, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-24, 0]], [[12, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249226
    {'center': '46656.a1', 'center_index': 46656, 'center_order': 1, 'counter': 130, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ir', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1', 'kernel_order': 1, 'label': '46656.ir.48j', 'nt': [144, 0], 'q_character': None, 'values': [[[48, 0]], [[16, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-24, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249227
    {'center': '46656.a1', 'center_index': 46656, 'center_order': 1, 'counter': 131, 'cyclotomic_n': 1, 'dim': 64, 'faithful': True, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ir', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1', 'kernel_order': 1, 'label': '46656.ir.64a', 'nt': [96, 0], 'q_character': None, 'values': [[[64, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-32, 0]], [[16, 0]], [[-32, 0]], [[-8, 0]], [[16, 0]], [[16, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[-8, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36249228
    {'center': '46656.a1', 'center_index': 46656, 'center_order': 1, 'counter': 132, 'cyclotomic_n': 1, 'dim': 64, 'faithful': True, 'field': [0, 1], 'group': '46656.ir', 'group_counter': 226, 'group_order': 46656, 'image': None, 'image_isoclass': '46656.ir', 'image_order': 46656, 'indicator': 1, 'kernel': '46656.a1', 'kernel_order': 1, 'label': '46656.ir.64b', 'nt': [96, 0], 'q_character': None, 'values': [[[64, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-32, 0]], [[-32, 0]], [[-8, 0]], [[16, 0]], [[-8, 0]], [[16, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 216712104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 46656, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '46656.ir.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', 'R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '46656.ir', 'subgroup_hash': 9168954550374180198, 'subgroup_order': 46656, 'subgroup_tex': 'C_3:S_3^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '23328.jw', 'subgroup_hash': 5373300810614188631, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:(D_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '23328.ih', 'subgroup_hash': 3566854269451973585, 'subgroup_order': 23328, 'subgroup_tex': '(C_3^2\\times S_3^3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '23328.ii', 'subgroup_hash': 1911315190739650868, 'subgroup_order': 23328, 'subgroup_tex': 'S_3^3:C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '23328.ja', 'subgroup_hash': 3997696643402362449, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '23328.iz', 'subgroup_hash': 8208275120894442370, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '23328.ix', 'subgroup_hash': 6476148778820911545, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 23328, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '23328.iy', 'subgroup_hash': 7163120604704803737, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 7776, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15552.lz', 'subgroup_hash': 4027828021754428216, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^4:C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '11664.le', 'subgroup_hash': 11985188565285282, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(A_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216712216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 11664, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.ld', 'subgroup_hash': 1572047044973151218, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^2\\times S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.lf', 'subgroup_hash': 1148176540360421445, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '11664.lb', 'subgroup_hash': 1672871540294440206, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '11664.lc', 'subgroup_hash': 1010523239180203268, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.jv', 'subgroup_hash': 3438986827836854046, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(C_4\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.ju', 'subgroup_hash': 27789121352440528, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(C_4\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.jw', 'subgroup_hash': 4051635583239640288, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.jx', 'subgroup_hash': 5231518508095151201, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.kq', 'subgroup_hash': 1226057760699008164, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216713216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 11664, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11664.lg', 'subgroup_hash': 4963073577443410154, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216713327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.4.l1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11664.hy', 'subgroup_hash': 6348664373455741994, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216713438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 7776, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kl', 'subgroup_hash': 1489488185878397060, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^2:C_4\\times S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 216713549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kl', 'subgroup_hash': 1489488185878397060, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^2:C_4\\times S_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 216713660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.cr', 'subgroup_hash': 5667679576347691602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713771
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.lb', 'subgroup_hash': 1212330179984271992, 'subgroup_order': 7776, 'subgroup_tex': 'S_3\\times C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kj', 'subgroup_hash': 6258479168115518834, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^3:C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kw', 'subgroup_hash': 9147545329350062181, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:(D_4\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216714104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kh', 'subgroup_hash': 175859787775777506, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.jo', 'subgroup_hash': 3487993102571590544, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kq', 'subgroup_hash': 219417612901070744, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.be', 'subgroup_hash': 4734684673362351397, 'subgroup_order': 7776, 'subgroup_tex': 'S_3^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216714549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3888, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kg', 'subgroup_hash': 6948233632470505448, 'subgroup_order': 7776, 'subgroup_tex': '(C_3\\times S_3^3):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3888, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.cr', 'subgroup_hash': 5667679576347691602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3888, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.jo', 'subgroup_hash': 3487993102571590544, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3888, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kq', 'subgroup_hash': 219417612901070744, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3888, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.kv', 'subgroup_hash': 1442755762403716510, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:(C_4\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216715104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3888, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.6.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7776.ku', 'subgroup_hash': 6346619599105731286, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 5832, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5832.ny', 'subgroup_hash': 3634481926712915960, 'subgroup_order': 5832, 'subgroup_tex': 'S_3^3:C_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 216715152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5832, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '5832.nz', 'subgroup_hash': 543144923730592804, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^4:(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 5832, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5832.mz', 'subgroup_hash': 1979516353938371657, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 5832, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5832.oc', 'subgroup_hash': 1071536843807771247, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5832, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5832.mv', 'subgroup_hash': 6296877844253508167, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^4:(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5832, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5832.oa', 'subgroup_hash': 3499632068993223770, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5832, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5832.mx', 'subgroup_hash': 3410761850773779731, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.ob', 'subgroup_hash': 6827146944380426314, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.iv', 'subgroup_hash': 7954818472351443286, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.iw', 'subgroup_hash': 1660486810505185516, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.hk', 'subgroup_hash': 3386641300099085764, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:(C_2\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216715263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.hv', 'subgroup_hash': 5832416579828807942, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^2\\wr C_2.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.iy', 'subgroup_hash': 3906279082698007701, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.ix', 'subgroup_hash': 4604337874228576908, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^5:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.rx', 'subgroup_hash': 915336683904724289, 'subgroup_order': 5184, 'subgroup_tex': 'S_3^2:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1296, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.9.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.og', 'subgroup_hash': 2215668191011695968, 'subgroup_order': 5184, 'subgroup_tex': 'C_4\\times S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3888, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jp', 'subgroup_hash': 3397237364168845709, 'subgroup_order': 3888, 'subgroup_tex': 'C_3:S_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216715330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3888, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kv', 'subgroup_hash': 2898379556612745707, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:(C_4\\times S_3^2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3888, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kw', 'subgroup_hash': 4147839145125586837, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jq', 'subgroup_hash': 539044406640765220, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2:C_{12}\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jt', 'subgroup_hash': 61003405795052071, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jp', 'subgroup_hash': 3397237364168845709, 'subgroup_order': 3888, 'subgroup_tex': 'C_3:S_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216715386
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jy', 'subgroup_hash': 3959595490248919829, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jy', 'subgroup_hash': 3959595490248919829, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.dv', 'subgroup_hash': 6670831907123181578, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.dv', 'subgroup_hash': 6670831907123181578, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.du', 'subgroup_hash': 3121236695664575994, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216715441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kl', 'subgroup_hash': 2314198597552979318, 'subgroup_order': 3888, 'subgroup_tex': 'S_3\\times C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kc', 'subgroup_hash': 1140259518669431859, 'subgroup_order': 3888, 'subgroup_tex': 'S_3\\times C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kk', 'subgroup_hash': 6894143851208483497, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_6\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.ke', 'subgroup_hash': 4133593436444144358, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715485
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jq', 'subgroup_hash': 539044406640765220, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2:C_{12}\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jt', 'subgroup_hash': 61003405795052071, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.de', 'subgroup_hash': 9038485956479665445, 'subgroup_order': 3888, 'subgroup_tex': '(C_3^2\\times S_3^2):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.df', 'subgroup_hash': 7816194596286507846, 'subgroup_order': 3888, 'subgroup_tex': '(C_3^3\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jz', 'subgroup_hash': 2114550812462024386, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.iv', 'subgroup_hash': 7404663447836067972, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.bt', 'subgroup_hash': 6945509031187788888, 'subgroup_order': 3888, 'subgroup_tex': 'S_3^4:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1944, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kd', 'subgroup_hash': 2363458476566927690, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\times S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1296, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.bs', 'subgroup_hash': 5230133027797992422, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\times S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.bx', 'subgroup_hash': 1584852141540622984, 'subgroup_order': 3888, 'subgroup_tex': '(C_3\\times S_3^3):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.bx', 'subgroup_hash': 1584852141540622984, 'subgroup_order': 3888, 'subgroup_tex': '(C_3\\times S_3^3):S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kl', 'subgroup_hash': 2314198597552979318, 'subgroup_order': 3888, 'subgroup_tex': 'S_3\\times C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.cb', 'subgroup_hash': 16080465424409965, 'subgroup_order': 3888, 'subgroup_tex': 'S_3\\times C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.bz', 'subgroup_hash': 957515932800553354, 'subgroup_order': 3888, 'subgroup_tex': 'S_3\\times C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jy', 'subgroup_hash': 3959595490248919829, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.dv', 'subgroup_hash': 6670831907123181578, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jq', 'subgroup_hash': 539044406640765220, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2:C_{12}\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.jt', 'subgroup_hash': 61003405795052071, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.de', 'subgroup_hash': 9038485956479665445, 'subgroup_order': 3888, 'subgroup_tex': '(C_3^2\\times S_3^2):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.df', 'subgroup_hash': 7816194596286507846, 'subgroup_order': 3888, 'subgroup_tex': '(C_3^3\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.ke', 'subgroup_hash': 4133593436444144358, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.il', 'subgroup_hash': 5553770281982022740, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216715730
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kv', 'subgroup_hash': 2898379556612745707, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:(C_4\\times S_3^2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kw', 'subgroup_hash': 4147839145125586837, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.dh', 'subgroup_hash': 4219826360563728225, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.dg', 'subgroup_hash': 7820937374858235473, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2\\wr C_2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.lb', 'subgroup_hash': 2700723428615589703, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^5.C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.lc', 'subgroup_hash': 772684872828353582, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^5:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715796
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.lc', 'subgroup_hash': 772684872828353582, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^5:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.ld', 'subgroup_hash': 5599066684545148362, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:C_{12}:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kz', 'subgroup_hash': 4201348917738129906, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2\\wr C_2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kx', 'subgroup_hash': 6041337051216539253, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^5:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.la', 'subgroup_hash': 1508313526865012668, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:C_{12}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.la', 'subgroup_hash': 1508313526865012668, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:C_{12}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.kb', 'subgroup_hash': 2802177873838975853, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216712150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.dh', 'subgroup_hash': 4219826360563728225, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.dg', 'subgroup_hash': 7820937374858235473, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2\\wr C_2.D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.iv', 'subgroup_hash': 7404663447836067972, 'subgroup_order': 3888, 'subgroup_tex': 'C_3\\wr C_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.bq', 'subgroup_hash': 5541825096805648039, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.ka', 'subgroup_hash': 1576939744793715357, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.12.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3888.by', 'subgroup_hash': 1872573129080097874, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 2916, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4', 'D', 'L1', 'D1', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2916.kw', 'subgroup_hash': 2747576288077165295, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.lt', 'subgroup_hash': 6948860401795433662, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.lp', 'subgroup_hash': 7835665494782961854, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4:(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 216712250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.lm', 'subgroup_hash': 2036151519078965009, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ha', 'subgroup_hash': 3072751048837029818, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ix', 'subgroup_hash': 8246389862659324385, 'subgroup_order': 2916, 'subgroup_tex': '(C_3^2\\times \\He_3):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.hb', 'subgroup_hash': 6466240489216709948, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.iw', 'subgroup_hash': 338372599056776571, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.lu', 'subgroup_hash': 5264986311775467971, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.lr', 'subgroup_hash': 7204522873303661722, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ls', 'subgroup_hash': 7429781159210229649, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ly', 'subgroup_hash': 2922831852738311910, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.lw', 'subgroup_hash': 759851528818786312, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\wr C_4:C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 216712361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.eb', 'subgroup_hash': 1125086880203529497, 'subgroup_order': 2592, 'subgroup_tex': 'C_3:S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ot', 'subgroup_hash': 3823451309511426102, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.or', 'subgroup_hash': 7986559567119365143, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.lw', 'subgroup_hash': 759851528818786312, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\wr C_4:C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 216712405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.lz', 'subgroup_hash': 4422668212765420530, 'subgroup_order': 2592, 'subgroup_tex': '(C_6\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712461
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.lw', 'subgroup_hash': 759851528818786312, 'subgroup_order': 2592, 'subgroup_tex': 'C_3\\wr C_4:C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 216712472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.eb', 'subgroup_hash': 1125086880203529497, 'subgroup_order': 2592, 'subgroup_tex': 'C_3:S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1296, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.cg', 'subgroup_hash': 1290607906254643219, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.jy', 'subgroup_hash': 5602630594461506265, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ki', 'subgroup_hash': 739205828648173786, 'subgroup_order': 2592, 'subgroup_tex': 'S_3\\wr C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.fs', 'subgroup_hash': 3641402233686599739, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^4:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216712527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.la', 'subgroup_hash': 8172602584111953953, 'subgroup_order': 2592, 'subgroup_tex': 'C_4\\times C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.kw', 'subgroup_hash': 4136029907869332243, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ky', 'subgroup_hash': 4787865736624930298, 'subgroup_order': 2592, 'subgroup_tex': 'C_4\\times C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ko', 'subgroup_hash': 4118049208961595371, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.18.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216712616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 1944, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3932', 'subgroup_hash': 3932, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3901', 'subgroup_hash': 3901, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216712638
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3939', 'subgroup_hash': 3939, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3940', 'subgroup_hash': 3940, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3933', 'subgroup_hash': 3933, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3937', 'subgroup_hash': 3937, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 972, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3894', 'subgroup_hash': 3894, 'subgroup_order': 1944, 'subgroup_tex': 'S_3\\times C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3895', 'subgroup_hash': 3895, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3895', 'subgroup_hash': 3895, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3898', 'subgroup_hash': 3898, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3936', 'subgroup_hash': 3936, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3932', 'subgroup_hash': 3932, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3938', 'subgroup_hash': 3938, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3938', 'subgroup_hash': 3938, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3894', 'subgroup_hash': 3894, 'subgroup_order': 1944, 'subgroup_tex': 'S_3\\times C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3898', 'subgroup_hash': 3898, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3904', 'subgroup_hash': 3904, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3933', 'subgroup_hash': 3933, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3907', 'subgroup_hash': 3907, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3908', 'subgroup_hash': 3908, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3936', 'subgroup_hash': 3936, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3910', 'subgroup_hash': 3910, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3914', 'subgroup_hash': 3914, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 648, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3880', 'subgroup_hash': 3880, 'subgroup_order': 1944, 'subgroup_tex': 'S_3^3:C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 216, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3880', 'subgroup_hash': 3880, 'subgroup_order': 1944, 'subgroup_tex': 'S_3^3:C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2344', 'subgroup_hash': 2344, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3882', 'subgroup_hash': 3882, 'subgroup_order': 1944, 'subgroup_tex': 'S_3\\times C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3937', 'subgroup_hash': 3937, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 972, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3894', 'subgroup_hash': 3894, 'subgroup_order': 1944, 'subgroup_tex': 'S_3\\times C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3895', 'subgroup_hash': 3895, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3895', 'subgroup_hash': 3895, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3898', 'subgroup_hash': 3898, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3933', 'subgroup_hash': 3933, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3570', 'subgroup_hash': 3570, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3491', 'subgroup_hash': 3491, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3495', 'subgroup_hash': 3495, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3482', 'subgroup_hash': 3482, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_2\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3488', 'subgroup_hash': 3488, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3902', 'subgroup_hash': 3902, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3902', 'subgroup_hash': 3902, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3939', 'subgroup_hash': 3939, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3896', 'subgroup_hash': 3896, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3896', 'subgroup_hash': 3896, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3899', 'subgroup_hash': 3899, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3897', 'subgroup_hash': 3897, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3899', 'subgroup_hash': 3899, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3897', 'subgroup_hash': 3897, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3900', 'subgroup_hash': 3900, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3900', 'subgroup_hash': 3900, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713160
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3903', 'subgroup_hash': 3903, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_2\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3905', 'subgroup_hash': 3905, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216713182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 972, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3896', 'subgroup_hash': 3896, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3897', 'subgroup_hash': 3897, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3899', 'subgroup_hash': 3899, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713217
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3900', 'subgroup_hash': 3900, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3482', 'subgroup_hash': 3482, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_2\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 216713239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3488', 'subgroup_hash': 3488, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3484', 'subgroup_hash': 3484, 'subgroup_order': 1944, 'subgroup_tex': '(C_3^2\\times D_9):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713261
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3938', 'subgroup_hash': 3938, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3936', 'subgroup_hash': 3936, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3910', 'subgroup_hash': 3910, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3914', 'subgroup_hash': 3914, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 972, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3908', 'subgroup_hash': 3908, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 648, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3876', 'subgroup_hash': 3876, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3906', 'subgroup_hash': 3906, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3940', 'subgroup_hash': 3940, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^2:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3915', 'subgroup_hash': 3915, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3916', 'subgroup_hash': 3916, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3901', 'subgroup_hash': 3901, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216713383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3902', 'subgroup_hash': 3902, 'subgroup_order': 1944, 'subgroup_tex': 'C_3\\wr C_4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3913', 'subgroup_hash': 3913, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3918', 'subgroup_hash': 3918, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3918', 'subgroup_hash': 3918, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3919', 'subgroup_hash': 3919, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 972, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3909', 'subgroup_hash': 3909, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 648, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3878', 'subgroup_hash': 3878, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3881', 'subgroup_hash': 3881, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216713472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3877', 'subgroup_hash': 3877, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3877', 'subgroup_hash': 3877, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3915', 'subgroup_hash': 3915, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3879', 'subgroup_hash': 3879, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3879', 'subgroup_hash': 3879, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 972, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.24.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3916', 'subgroup_hash': 3916, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.27.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47869', 'subgroup_hash': 47869, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216713550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47045', 'subgroup_hash': 47045, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216713561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1728.46586', 'subgroup_hash': 46586, 'subgroup_order': 1728, 'subgroup_tex': 'C_4\\times S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216713572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1643', 'subgroup_hash': 1643, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1647', 'subgroup_hash': 1647, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1644', 'subgroup_hash': 1644, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1650', 'subgroup_hash': 1650, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1649', 'subgroup_hash': 1649, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1646', 'subgroup_hash': 1646, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1652', 'subgroup_hash': 1652, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 1296, 'counter': 239, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '46656.ir.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3490', 'subgroup_hash': 3490, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3564', 'subgroup_hash': 3564, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_{12}\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3565', 'subgroup_hash': 3565, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3583', 'subgroup_hash': 3583, 'subgroup_order': 1296, 'subgroup_tex': 'C_6:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3566', 'subgroup_hash': 3566, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216713705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3566', 'subgroup_hash': 3566, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216713716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3567', 'subgroup_hash': 3567, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216713727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3567', 'subgroup_hash': 3567, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216713738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3568', 'subgroup_hash': 3568, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:(C_2^2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216713749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3572', 'subgroup_hash': 3572, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3575', 'subgroup_hash': 3575, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3538', 'subgroup_hash': 3538, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3564', 'subgroup_hash': 3564, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_{12}\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3565', 'subgroup_hash': 3565, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3583', 'subgroup_hash': 3583, 'subgroup_order': 1296, 'subgroup_tex': 'C_6:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713871
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3526', 'subgroup_hash': 3526, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3529', 'subgroup_hash': 3529, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3564', 'subgroup_hash': 3564, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_{12}\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3565', 'subgroup_hash': 3565, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3525', 'subgroup_hash': 3525, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3526', 'subgroup_hash': 3526, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216713960
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216713982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216713994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3528', 'subgroup_hash': 3528, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3583', 'subgroup_hash': 3583, 'subgroup_order': 1296, 'subgroup_tex': 'C_6:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3569', 'subgroup_hash': 3569, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^2:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3572', 'subgroup_hash': 3572, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3494', 'subgroup_hash': 3494, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3538', 'subgroup_hash': 3538, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216714138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 216, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3525', 'subgroup_hash': 3525, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3526', 'subgroup_hash': 3526, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216714160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3490', 'subgroup_hash': 3490, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216714171
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3490', 'subgroup_hash': 3490, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216714182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.838', 'subgroup_hash': 838, 'subgroup_order': 1296, 'subgroup_tex': 'C_4\\times C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3493', 'subgroup_hash': 3493, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3492', 'subgroup_hash': 3492, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3091', 'subgroup_hash': 3091, 'subgroup_order': 1296, 'subgroup_tex': 'C_4\\times C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3087', 'subgroup_hash': 3087, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3086', 'subgroup_hash': 3086, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times C_6).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3083', 'subgroup_hash': 3083, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times C_6).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3526', 'subgroup_hash': 3526, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^3:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216714271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3529', 'subgroup_hash': 3529, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216714282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3566', 'subgroup_hash': 3566, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216714293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3567', 'subgroup_hash': 3567, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 216714304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3564', 'subgroup_hash': 3564, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_{12}\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3565', 'subgroup_hash': 3565, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714461
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714472
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714516
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3496', 'subgroup_hash': 3496, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714527
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3496', 'subgroup_hash': 3496, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3496', 'subgroup_hash': 3496, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3500', 'subgroup_hash': 3500, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3500', 'subgroup_hash': 3500, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3496', 'subgroup_hash': 3496, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3500', 'subgroup_hash': 3500, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3500', 'subgroup_hash': 3500, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3528', 'subgroup_hash': 3528, 'subgroup_order': 1296, 'subgroup_tex': 'S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 216714683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3490', 'subgroup_hash': 3490, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216714694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216714705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3530', 'subgroup_hash': 3530, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216714716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 648, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.36.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3490', 'subgroup_hash': 3490, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216714727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 972, 'counter': 336, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 972, 'counter': 337, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.878', 'subgroup_hash': 878, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216714749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 972, 'counter': 338, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.881', 'subgroup_hash': 881, 'subgroup_order': 972, 'subgroup_tex': 'C_3^5:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 972, 'counter': 339, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.886', 'subgroup_hash': 886, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.885', 'subgroup_hash': 885, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.884', 'subgroup_hash': 884, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.885', 'subgroup_hash': 885, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.887', 'subgroup_hash': 887, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.887', 'subgroup_hash': 887, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.890', 'subgroup_hash': 890, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.884', 'subgroup_hash': 884, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.437', 'subgroup_hash': 437, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.438', 'subgroup_hash': 438, 'subgroup_order': 972, 'subgroup_tex': '\\He_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.461', 'subgroup_hash': 461, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.885', 'subgroup_hash': 885, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.810', 'subgroup_hash': 810, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.788', 'subgroup_hash': 788, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.888', 'subgroup_hash': 888, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.888', 'subgroup_hash': 888, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.788', 'subgroup_hash': 788, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.792', 'subgroup_hash': 792, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.879', 'subgroup_hash': 879, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216714971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.879', 'subgroup_hash': 879, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216714982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.880', 'subgroup_hash': 880, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216714994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 486, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.880', 'subgroup_hash': 880, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.760', 'subgroup_hash': 760, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.772', 'subgroup_hash': 772, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.767', 'subgroup_hash': 767, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.767', 'subgroup_hash': 767, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.761', 'subgroup_hash': 761, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4.C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.769', 'subgroup_hash': 769, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times C_9):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 486, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.885', 'subgroup_hash': 885, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.887', 'subgroup_hash': 887, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.887', 'subgroup_hash': 887, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.890', 'subgroup_hash': 890, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.884', 'subgroup_hash': 884, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.781', 'subgroup_hash': 781, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.436', 'subgroup_hash': 436, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.460', 'subgroup_hash': 460, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.460', 'subgroup_hash': 460, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.816', 'subgroup_hash': 816, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.806', 'subgroup_hash': 806, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.893', 'subgroup_hash': 893, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.459', 'subgroup_hash': 459, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.459', 'subgroup_hash': 459, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.893', 'subgroup_hash': 893, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.886', 'subgroup_hash': 886, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.889', 'subgroup_hash': 889, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.889', 'subgroup_hash': 889, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.892', 'subgroup_hash': 892, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.892', 'subgroup_hash': 892, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.878', 'subgroup_hash': 878, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.879', 'subgroup_hash': 879, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.880', 'subgroup_hash': 880, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.881', 'subgroup_hash': 881, 'subgroup_order': 972, 'subgroup_tex': 'C_3^5:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.877', 'subgroup_hash': 877, 'subgroup_order': 972, 'subgroup_tex': 'C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.877', 'subgroup_hash': 877, 'subgroup_order': 972, 'subgroup_tex': 'C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.889', 'subgroup_hash': 889, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.891', 'subgroup_hash': 891, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.806', 'subgroup_hash': 806, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715160
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.892', 'subgroup_hash': 892, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.480', 'subgroup_hash': 480, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.882', 'subgroup_hash': 882, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.48.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.883', 'subgroup_hash': 883, 'subgroup_order': 972, 'subgroup_tex': 'C_3^5:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4698', 'subgroup_hash': 4698, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4470', 'subgroup_hash': 4470, 'subgroup_order': 864, 'subgroup_tex': 'D_4\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4483', 'subgroup_hash': 4483, 'subgroup_order': 864, 'subgroup_tex': 'C_3^3:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4240', 'subgroup_hash': 4240, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4241', 'subgroup_hash': 4241, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4367', 'subgroup_hash': 4367, 'subgroup_order': 864, 'subgroup_tex': 'C_4\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4074', 'subgroup_hash': 4074, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4223', 'subgroup_hash': 4223, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4075', 'subgroup_hash': 4075, 'subgroup_order': 864, 'subgroup_tex': 'D_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4698', 'subgroup_hash': 4698, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4239', 'subgroup_hash': 4239, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4691', 'subgroup_hash': 4691, 'subgroup_order': 864, 'subgroup_tex': 'C_6:S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4689', 'subgroup_hash': 4689, 'subgroup_order': 864, 'subgroup_tex': 'C_2\\times C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4688', 'subgroup_hash': 4688, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:C_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4223', 'subgroup_hash': 4223, 'subgroup_order': 864, 'subgroup_tex': 'S_3\\times C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4224', 'subgroup_hash': 4224, 'subgroup_order': 864, 'subgroup_tex': 'C_{12}:S_3.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4550', 'subgroup_hash': 4550, 'subgroup_order': 864, 'subgroup_tex': 'C_6.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4698', 'subgroup_hash': 4698, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4239', 'subgroup_hash': 4239, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4251', 'subgroup_hash': 4251, 'subgroup_order': 864, 'subgroup_tex': 'C_{12}\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4076', 'subgroup_hash': 4076, 'subgroup_order': 864, 'subgroup_tex': 'C_3^3:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4279', 'subgroup_hash': 4279, 'subgroup_order': 864, 'subgroup_tex': 'C_4\\times S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4077', 'subgroup_hash': 4077, 'subgroup_order': 864, 'subgroup_tex': 'S_3^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4686', 'subgroup_hash': 4686, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4686', 'subgroup_hash': 4686, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4367', 'subgroup_hash': 4367, 'subgroup_order': 864, 'subgroup_tex': 'C_4\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4074', 'subgroup_hash': 4074, 'subgroup_order': 864, 'subgroup_tex': 'S_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4279', 'subgroup_hash': 4279, 'subgroup_order': 864, 'subgroup_tex': 'C_4\\times S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4077', 'subgroup_hash': 4077, 'subgroup_order': 864, 'subgroup_tex': 'S_3^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4309', 'subgroup_hash': 4309, 'subgroup_order': 864, 'subgroup_tex': 'C_4\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4078', 'subgroup_hash': 4078, 'subgroup_order': 864, 'subgroup_tex': 'C_3^3:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4240', 'subgroup_hash': 4240, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4241', 'subgroup_hash': 4241, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4668', 'subgroup_hash': 4668, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4668', 'subgroup_hash': 4668, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4668', 'subgroup_hash': 4668, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4668', 'subgroup_hash': 4668, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4225', 'subgroup_hash': 4225, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:C_4\\times D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.54.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4226', 'subgroup_hash': 4226, 'subgroup_order': 864, 'subgroup_tex': '(C_3^2\\times D_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '46656.ir.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.479', 'subgroup_hash': 479, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 3}
  • id: 216715210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 648, 'counter': 441, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 648, 'counter': 442, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.704', 'subgroup_hash': 704, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 648, 'counter': 443, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.703', 'subgroup_hash': 703, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.747', 'subgroup_hash': 747, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.750', 'subgroup_hash': 750, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.742', 'subgroup_hash': 742, 'subgroup_order': 648, 'subgroup_tex': 'C_6\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715216
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.743', 'subgroup_hash': 743, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715217
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.743', 'subgroup_hash': 743, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.744', 'subgroup_hash': 744, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.749', 'subgroup_hash': 749, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.746', 'subgroup_hash': 746, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.751', 'subgroup_hash': 751, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.751', 'subgroup_hash': 751, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.742', 'subgroup_hash': 742, 'subgroup_order': 648, 'subgroup_tex': 'C_6\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.744', 'subgroup_hash': 744, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.745', 'subgroup_hash': 745, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715228
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.747', 'subgroup_hash': 747, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.749', 'subgroup_hash': 749, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.746', 'subgroup_hash': 746, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.747', 'subgroup_hash': 747, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.749', 'subgroup_hash': 749, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.746', 'subgroup_hash': 746, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 216, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 216, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.299', 'subgroup_hash': 299, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.128', 'subgroup_hash': 128, 'subgroup_order': 648, 'subgroup_tex': 'C_4\\times C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.65', 'subgroup_hash': 65, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 216715282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.130', 'subgroup_hash': 130, 'subgroup_order': 648, 'subgroup_tex': 'C_4\\times C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.67', 'subgroup_hash': 67, 'subgroup_order': 648, 'subgroup_tex': '\\He_3:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 216715284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.706', 'subgroup_hash': 706, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.180', 'subgroup_hash': 180, 'subgroup_order': 648, 'subgroup_tex': 'C_4\\times C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.66', 'subgroup_hash': 66, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 216715288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.731', 'subgroup_hash': 731, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.555', 'subgroup_hash': 555, 'subgroup_order': 648, 'subgroup_tex': 'C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.750', 'subgroup_hash': 750, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.742', 'subgroup_hash': 742, 'subgroup_order': 648, 'subgroup_tex': 'C_6\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.743', 'subgroup_hash': 743, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.743', 'subgroup_hash': 743, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.744', 'subgroup_hash': 744, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.747', 'subgroup_hash': 747, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.540', 'subgroup_hash': 540, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:C_4\\times D_9', 'supersolvable': False, 'sylow': 0}
  • id: 216715376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.751', 'subgroup_hash': 751, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.733', 'subgroup_hash': 733, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.749', 'subgroup_hash': 749, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.719', 'subgroup_hash': 719, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.722', 'subgroup_hash': 722, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 216715407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.720', 'subgroup_hash': 720, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.720', 'subgroup_hash': 720, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.705', 'subgroup_hash': 705, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 216715424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.734', 'subgroup_hash': 734, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.722', 'subgroup_hash': 722, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.704', 'subgroup_hash': 704, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.704', 'subgroup_hash': 704, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.723', 'subgroup_hash': 723, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 324, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.703', 'subgroup_hash': 703, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.72.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.703', 'subgroup_hash': 703, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8523', 'subgroup_hash': 8523, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2:(C_2^2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 216715433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8389', 'subgroup_hash': 8389, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715434
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 486, 'counter': 643, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 486, 'counter': 644, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.258', 'subgroup_hash': 258, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 486, 'counter': 645, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.96.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.256', 'subgroup_hash': 256, 'subgroup_order': 486, 'subgroup_tex': 'S_3\\times C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216715438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.117', 'subgroup_hash': 117, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.231', 'subgroup_hash': 231, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.233', 'subgroup_hash': 233, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 243, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.256', 'subgroup_hash': 256, 'subgroup_order': 486, 'subgroup_tex': 'S_3\\times C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216715443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.115', 'subgroup_hash': 115, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.115', 'subgroup_hash': 115, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.222', 'subgroup_hash': 222, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.116', 'subgroup_hash': 116, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.116', 'subgroup_hash': 116, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.222', 'subgroup_hash': 222, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.224', 'subgroup_hash': 224, 'subgroup_order': 486, 'subgroup_tex': 'D_9:C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.165', 'subgroup_hash': 165, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.258', 'subgroup_hash': 258, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.166', 'subgroup_hash': 166, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.166', 'subgroup_hash': 166, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.258', 'subgroup_hash': 258, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.248', 'subgroup_hash': 248, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715460
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.259', 'subgroup_hash': 259, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.167', 'subgroup_hash': 167, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.167', 'subgroup_hash': 167, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.242', 'subgroup_hash': 242, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.185', 'subgroup_hash': 185, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.185', 'subgroup_hash': 185, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.185', 'subgroup_hash': 185, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.185', 'subgroup_hash': 185, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.259', 'subgroup_hash': 259, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.242', 'subgroup_hash': 242, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.96.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.244', 'subgroup_hash': 244, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715472
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715475
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.765', 'subgroup_hash': 765, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.766', 'subgroup_hash': 766, 'subgroup_order': 432, 'subgroup_tex': 'C_2^2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715477
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715478
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715479
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.768', 'subgroup_hash': 768, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.714', 'subgroup_hash': 714, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715489
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.765', 'subgroup_hash': 765, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.766', 'subgroup_hash': 766, 'subgroup_order': 432, 'subgroup_tex': 'C_2^2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.724', 'subgroup_hash': 724, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.648', 'subgroup_hash': 648, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.594', 'subgroup_hash': 594, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715500
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.670', 'subgroup_hash': 670, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715502
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.595', 'subgroup_hash': 595, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715503
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.595', 'subgroup_hash': 595, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715505
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.768', 'subgroup_hash': 768, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.764', 'subgroup_hash': 764, 'subgroup_order': 432, 'subgroup_tex': 'C_6:S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.670', 'subgroup_hash': 670, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.684', 'subgroup_hash': 684, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.760', 'subgroup_hash': 760, 'subgroup_order': 432, 'subgroup_tex': 'A_4:C_6^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.762', 'subgroup_hash': 762, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.671', 'subgroup_hash': 671, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.768', 'subgroup_hash': 768, 'subgroup_order': 432, 'subgroup_tex': 'C_3:D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.704', 'subgroup_hash': 704, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.684', 'subgroup_hash': 684, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.754', 'subgroup_hash': 754, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.648', 'subgroup_hash': 648, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.594', 'subgroup_hash': 594, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.574', 'subgroup_hash': 574, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.580', 'subgroup_hash': 580, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.754', 'subgroup_hash': 754, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.759', 'subgroup_hash': 759, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 216, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.670', 'subgroup_hash': 670, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.595', 'subgroup_hash': 595, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.648', 'subgroup_hash': 648, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.594', 'subgroup_hash': 594, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.574', 'subgroup_hash': 574, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.580', 'subgroup_hash': 580, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.755', 'subgroup_hash': 755, 'subgroup_order': 432, 'subgroup_tex': 'S_3^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.300', 'subgroup_hash': 300, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.690', 'subgroup_hash': 690, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.596', 'subgroup_hash': 596, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.630', 'subgroup_hash': 630, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.637', 'subgroup_hash': 637, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.567', 'subgroup_hash': 567, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.575', 'subgroup_hash': 575, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.587', 'subgroup_hash': 587, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.567', 'subgroup_hash': 567, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.581', 'subgroup_hash': 581, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715570
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.581', 'subgroup_hash': 581, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715571
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.756', 'subgroup_hash': 756, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.690', 'subgroup_hash': 690, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.596', 'subgroup_hash': 596, 'subgroup_order': 432, 'subgroup_tex': 'C_2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.579', 'subgroup_hash': 579, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.586', 'subgroup_hash': 586, 'subgroup_order': 432, 'subgroup_tex': 'C_6.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216715577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.765', 'subgroup_hash': 765, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.634', 'subgroup_hash': 634, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.766', 'subgroup_hash': 766, 'subgroup_order': 432, 'subgroup_tex': 'C_2^2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.641', 'subgroup_hash': 641, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_6^2):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.685', 'subgroup_hash': 685, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.568', 'subgroup_hash': 568, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times D_6):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.568', 'subgroup_hash': 568, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times D_6):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.630', 'subgroup_hash': 630, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.567', 'subgroup_hash': 567, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.631', 'subgroup_hash': 631, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times C_{12}):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.637', 'subgroup_hash': 637, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.638', 'subgroup_hash': 638, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.569', 'subgroup_hash': 569, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_{12}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.567', 'subgroup_hash': 567, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216715610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.569', 'subgroup_hash': 569, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_{12}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.744', 'subgroup_hash': 744, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.744', 'subgroup_hash': 744, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.743', 'subgroup_hash': 743, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times A_4):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.743', 'subgroup_hash': 743, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times A_4):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.672', 'subgroup_hash': 672, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.568', 'subgroup_hash': 568, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times D_6):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.568', 'subgroup_hash': 568, 'subgroup_order': 432, 'subgroup_tex': '(C_3^2\\times D_6):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.686', 'subgroup_hash': 686, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216715629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.673', 'subgroup_hash': 673, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.108.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 216715633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 324, 'counter': 822, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.191', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 191, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C5', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.172', 'subgroup_hash': 172, 'subgroup_order': 324, 'subgroup_tex': 'D_6\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.174', 'subgroup_hash': 174, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715638
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.174', 'subgroup_hash': 174, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.175', 'subgroup_hash': 175, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.172', 'subgroup_hash': 172, 'subgroup_order': 324, 'subgroup_tex': 'D_6\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715661
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.172', 'subgroup_hash': 172, 'subgroup_order': 324, 'subgroup_tex': 'D_6\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715668
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.68', 'subgroup_hash': 68, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.69', 'subgroup_hash': 69, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.77', 'subgroup_hash': 77, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.31', 'subgroup_hash': 31, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216715675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.13', 'subgroup_hash': 13, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216715676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.14', 'subgroup_hash': 14, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216715677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.22', 'subgroup_hash': 22, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715678
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.118', 'subgroup_hash': 118, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715702
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715703
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.119', 'subgroup_hash': 119, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 216715706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715711
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715712
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715714
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715725
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715726
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715728
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715729
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715731
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715733
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.109', 'subgroup_hash': 109, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_{36}', 'supersolvable': False, 'sylow': 0}
  • id: 216715735
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.112', 'subgroup_hash': 112, 'subgroup_order': 324, 'subgroup_tex': '(C_3^2\\times C_9):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715736
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715737
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.174', 'subgroup_hash': 174, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.174', 'subgroup_hash': 174, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.175', 'subgroup_hash': 175, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715747
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715748
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.172', 'subgroup_hash': 172, 'subgroup_order': 324, 'subgroup_tex': 'D_6\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216715765
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715766
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.117', 'subgroup_hash': 117, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.124', 'subgroup_hash': 124, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715789
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715795
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715797
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216715822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.160', 'subgroup_hash': 160, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216715827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.167', 'subgroup_hash': 167, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.121', 'subgroup_hash': 121, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.39', 'subgroup_hash': 39, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.144.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.932', 'subgroup_hash': 932, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.882', 'subgroup_hash': 882, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1039', 'subgroup_hash': 1039, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.932', 'subgroup_hash': 932, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.933', 'subgroup_hash': 933, 'subgroup_order': 288, 'subgroup_tex': '(C_6\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1039', 'subgroup_hash': 1039, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.941', 'subgroup_hash': 941, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.880', 'subgroup_hash': 880, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 1050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.162.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712164
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 243, 'counter': 1052, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1469', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1469, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4.D_6', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
  • id: 216712165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.192.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.51', 'subgroup_hash': 51, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.192.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.51', 'subgroup_hash': 51, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.192.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.51', 'subgroup_hash': 51, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.192.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.51', 'subgroup_hash': 51, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 1057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.192.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.192.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.63', 'subgroup_hash': 63, 'subgroup_order': 243, 'subgroup_tex': 'C_9:C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 216, 'counter': 1059, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.156', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 156, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.175', 'subgroup_hash': 175, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712195
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.175', 'subgroup_hash': 175, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.151', 'subgroup_hash': 151, 'subgroup_order': 216, 'subgroup_tex': 'D_4\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.149', 'subgroup_hash': 149, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.136', 'subgroup_hash': 136, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.124', 'subgroup_hash': 124, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.173', 'subgroup_hash': 173, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.136', 'subgroup_hash': 136, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.124', 'subgroup_hash': 124, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.136', 'subgroup_hash': 136, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.124', 'subgroup_hash': 124, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.102', 'subgroup_hash': 102, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.67', 'subgroup_hash': 67, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.50', 'subgroup_hash': 50, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.146', 'subgroup_hash': 146, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.141', 'subgroup_hash': 141, 'subgroup_order': 216, 'subgroup_tex': 'C_3:S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.125', 'subgroup_hash': 125, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.131', 'subgroup_hash': 131, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.131', 'subgroup_hash': 131, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 1178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.141', 'subgroup_hash': 141, 'subgroup_order': 216, 'subgroup_tex': 'C_3:S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.125', 'subgroup_hash': 125, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.131', 'subgroup_hash': 131, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.50', 'subgroup_hash': 50, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 1201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 1205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 1207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.175', 'subgroup_hash': 175, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 1214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 1218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 1221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 1227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 1229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 1234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.141', 'subgroup_hash': 141, 'subgroup_order': 216, 'subgroup_tex': 'C_3:S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.125', 'subgroup_hash': 125, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712386
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712390
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712391
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712396
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 1263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 1265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 1269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.172', 'subgroup_hash': 172, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.176', 'subgroup_hash': 176, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.149', 'subgroup_hash': 149, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 1295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712434
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.127', 'subgroup_hash': 127, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216712437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.142', 'subgroup_hash': 142, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.146', 'subgroup_hash': 146, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.147', 'subgroup_hash': 147, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.137', 'subgroup_hash': 137, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.127', 'subgroup_hash': 127, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216712457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712465
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712467
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712468
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 1341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712486
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 1342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 1343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.158', 'subgroup_hash': 158, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 216712488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 1344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.216.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.159', 'subgroup_hash': 159, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1469', 'subgroup_hash': 1469, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712490
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.243.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1103', 'subgroup_hash': 1103, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 1347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.55', 'subgroup_hash': 55, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 1348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712493
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 1349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 1350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 1351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 1352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.28', 'subgroup_hash': 28, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 1354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712501
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.37', 'subgroup_hash': 37, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712502
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 1357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712503
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 1358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 18, 'counter': 1359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 1360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 1361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.39', 'subgroup_hash': 39, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 216712508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 1362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.55', 'subgroup_hash': 55, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 1363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 1364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 1365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 1366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712513
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 1367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 1368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 1369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 1370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.10', 'subgroup_hash': 10, 'subgroup_order': 162, 'subgroup_tex': 'C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.10', 'subgroup_hash': 10, 'subgroup_order': 162, 'subgroup_tex': 'C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 1374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 1380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 1381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.11', 'subgroup_hash': 11, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 1382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.11', 'subgroup_hash': 11, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 1386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 1390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216712540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 1392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 1397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.32', 'subgroup_hash': 32, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216712551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.19', 'subgroup_hash': 19, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 1402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 1407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216712560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.10', 'subgroup_hash': 10, 'subgroup_order': 162, 'subgroup_tex': 'C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 1410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.10', 'subgroup_hash': 10, 'subgroup_order': 162, 'subgroup_tex': 'C_3\\wr S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 1416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 1420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.11', 'subgroup_hash': 11, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.11', 'subgroup_hash': 11, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 1431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 1438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 1446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.19', 'subgroup_hash': 19, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 1448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.19', 'subgroup_hash': 19, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.19', 'subgroup_hash': 19, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.19', 'subgroup_hash': 19, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.19', 'subgroup_hash': 19, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ea2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ea2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.19', 'subgroup_hash': 19, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 1453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 1455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.288.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.45', 'subgroup_hash': 45, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216712612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712622
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 1465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712624
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 1468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 1481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 216712663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712702
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712707
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712714
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.116', 'subgroup_hash': 116, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.116', 'subgroup_hash': 116, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.116', 'subgroup_hash': 116, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.116', 'subgroup_hash': 116, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216712722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.115', 'subgroup_hash': 115, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712733
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 1566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712735
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 1575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.133', 'subgroup_hash': 133, 'subgroup_order': 144, 'subgroup_tex': '(C_3\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.133', 'subgroup_hash': 133, 'subgroup_order': 144, 'subgroup_tex': '(C_3\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.133', 'subgroup_hash': 133, 'subgroup_order': 144, 'subgroup_tex': '(C_3\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.133', 'subgroup_hash': 133, 'subgroup_order': 144, 'subgroup_tex': '(C_3\\times C_{12}):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 1584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.136', 'subgroup_hash': 136, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.324.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 216712767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 108, 'counter': 1596, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '432.753', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 753, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712779
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712789
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712795
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712796
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712797
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 1624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712807
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 1634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712851
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.35', 'subgroup_hash': 35, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.34', 'subgroup_hash': 34, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216712855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.13', 'subgroup_hash': 13, 'subgroup_order': 108, 'subgroup_tex': 'C_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216712858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216712859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216712864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216712885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 1702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 1710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 36, 'counter': 1718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 1720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 1722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 1723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712910
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712912
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 36, 'counter': 1726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 1727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 1730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712918
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 1733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 1734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 1737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 1738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 1740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216712929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 1741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216712930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 1768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712969
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712989
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hq2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hq2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216712998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216712999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 1825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713030
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 1832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.35', 'subgroup_hash': 35, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.34', 'subgroup_hash': 34, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 1854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 1855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713080
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 1878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 1898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713110
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ly1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.lz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ma1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ma1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.md1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.md1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.me1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.me1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 1916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 1917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 1918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 1920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.mk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.mk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 1921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.432.ml1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.ml1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 216713140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.194', 'subgroup_hash': 194, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.78', 'subgroup_hash': 78, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.80', 'subgroup_hash': 80, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.486.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.100', 'subgroup_hash': 100, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713156
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 1946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713157
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 1947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713158
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 1948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713159
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 1949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713167
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 9, 'counter': 1956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 9, 'counter': 1957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713169
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 1958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713170
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 1959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 216713172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 1960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 216713173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 1961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 1962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.576.t2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.t2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 1971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 1977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 36, 'counter': 1979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 1980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713195
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 1981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 1982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713206
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713207
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 1994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 1995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713222
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 2009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713235
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713255
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713257
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713258
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713260
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713262
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713263
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713264
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713266
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713267
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713269
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713287
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.5', 'subgroup_hash': 5, 'subgroup_order': 72, 'subgroup_tex': 'C_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216713367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 2149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713386
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713388
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 2154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713389
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 2155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713390
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713391
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 2158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 2160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713396
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 2169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 2172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713440
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713463
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713465
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713467
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216713475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713479
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.648.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 216713493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2249, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '46656.ir.729.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '729.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 216713495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 54, 'counter': 2250, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.864.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '864.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '864.4668', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4668, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 2254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 2255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713502
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713503
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 9, 'counter': 2260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.m2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 27, 'counter': 2265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 2266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 216713521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 2274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 2275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 2276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 2277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713528
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 2282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 2283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713532
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 2284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 2290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713541
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 2293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 2294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 27, 'counter': 2297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 2302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 2306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 2313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 2318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 2319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 2322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713576
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 2323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 2330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 2331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 2332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 2333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216713591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 2338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 2345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 2355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 2360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713622
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 2365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 2371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 2372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713637
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ex2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ex2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 2382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 2390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713665
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 2404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713667
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 2405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713668
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 27, 'counter': 2410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713678
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713679
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713681
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713682
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713688
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 2424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713689
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 2431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gt2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gt2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713702
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216713703
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216713704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713707
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 2442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 2443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 2444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.864.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713712
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713714
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713718
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713729
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713747
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713748
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713765
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713766
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713769
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216713774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713779
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713796
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713797
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216713807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.972.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': True, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 36, 'counter': 2541, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '46656.ir.1296.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1296.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1296.3490', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3490, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\wr S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 2545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713823
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713824
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713825
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 2548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 2552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 2580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713862
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713910
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 216713912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713914
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713918
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713921
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713932
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216713937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713939
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2650, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 216713940
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216713941
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 2669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 2670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 2671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 18, 'counter': 2673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 2674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 2675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 2676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 2677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216713969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216713970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713989
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713998
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216713999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714006
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 2710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714020
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ho1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ho1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ht1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ht1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.hz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.hz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ia1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ia1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ib1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ib1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ic1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ic1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.id1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.id1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ie1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ie1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.if1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.if1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ig1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ig1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ih1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ih1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ii1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ii1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ij1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ij1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ik1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ik1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.il1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.il1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.im1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.im1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 2764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.in1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.in1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.io1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.io1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ip1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ip1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.iq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ir1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ir1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.is1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.is1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.it1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.it1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.iu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.iv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.iw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714076
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ix1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.ix1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.iy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.iz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.iz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ja1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ja1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714080
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.jb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714083
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 2780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.jd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714084
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.je1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.je1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ji1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ji1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.js1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.js1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ju1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ju1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.jz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.jz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ka1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ka1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714110
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 2804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.kb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ke1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ke1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ki1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ki1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.km1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.km1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ko1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ko1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ks1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ks1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ku1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ku1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ky1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ky1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.kz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.kz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.la1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.la1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ld1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ld1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.le1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.le1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.li1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.li1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ll1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ll1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ln1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ln1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ls1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ls1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714159
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 2849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 2850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 2853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.ly1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.ly1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1296.lz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.lz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714166
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714168
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714176
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1458.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 27, 'counter': 2870, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.1728.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1728.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1728.47869', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47869, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1728, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:(C_4\\times D_6)', 'simple': False, 'solvable': True, 'special_labels': ['D3', 'C7', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714185
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714187
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714188
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714189
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714190
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714191
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714192
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714194
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 216714195
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 216714196
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714197
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 2883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714198
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714199
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 2885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 9, 'counter': 2886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': False, 'core_order': 9, 'counter': 2887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 9, 'counter': 2888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714203
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 2889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714205
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714206
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714207
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714214
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 2903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714221
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714222
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 2905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1728.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.bh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714223
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714233
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714242
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714247
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714252
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 2934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 2935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 2936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 2937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714261
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714262
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 2943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 2944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 2946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714269
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 2949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714277
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 2957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714289
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714290
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714295
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714297
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 2973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714299
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714300
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714301
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714303
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 2982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 2988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714314
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714319
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 2993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 2995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 2996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 2999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714331
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714336
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714340
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714377
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714396
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714397
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714399
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714421
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714424
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.ha1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.ha1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.hb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.hb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.hc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.hc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.hd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.hd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.he1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.he1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.hf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.hf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.hg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.hg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.hh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.hh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.1944.hi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1944.hi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 18, 'counter': 3097, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.2592.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2592.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2592.cg', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1290607906254643219, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2592, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714436
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714437
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714440
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714442
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 9, 'counter': 3102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714443
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714444
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714458
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 216714459
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714460
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714463
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714464
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 9, 'counter': 3128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714478
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714479
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714485
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714486
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714488
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 3144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 3147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714493
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714497
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 3152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714498
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714500
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 3158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714504
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714506
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714507
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714508
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714513
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 3168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714517
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714518
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714522
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 3177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714528
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714529
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216714530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 3191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 3200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 3202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714559
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 3208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714560
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714565
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 3218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.et2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.et2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 3226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 3233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714595
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fo2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fo2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 3255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 3264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714622
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714624
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714628
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216714629
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 216714630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2592.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 216714639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714642
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 216714656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714658
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714663
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714673
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714677
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.2916.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714699
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714702
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714707
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714711
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714712
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714713
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714718
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714728
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714729
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714731
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714733
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714735
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714736
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714743
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3374, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714744
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3375, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714745
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714746
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3377, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714747
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714748
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3379, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714750
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714751
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714752
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3382, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714753
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3383, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714754
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714755
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714756
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3386, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714757
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3387, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714758
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3388, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714759
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714761
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714762
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714763
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3392, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714764
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714765
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3394, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714766
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714767
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3396, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714768
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714781
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714789
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714795
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714796
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714798
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714807
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714810
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714826
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714835
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3457, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714836
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3458, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714837
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714839
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714840
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3461, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714841
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714842
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3463, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714843
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714844
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3465, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714845
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 3476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 216714857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714859
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714861
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714862
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3494, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3888.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 216714877
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.3888.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3888.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3888, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 11664, 'characteristic': True, 'core_order': 9, 'counter': 3496, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '46656.ir.5184.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5184.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '5184.og', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2215668191011695968, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5184, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times S_3\\wr S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714879
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 1, 'counter': 3497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714880
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': False, 'core_order': 1, 'counter': 3498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 3499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 1, 'counter': 3500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': False, 'core_order': 1, 'counter': 3501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 3502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714887
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714888
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 1, 'counter': 3505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 1, 'counter': 3508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 3509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714895
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714896
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 3511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714897
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714898
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714899
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3514, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 216714900
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3515, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 216714901
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 3518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714904
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714906
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.x2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 3522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714909
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 3523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 3525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5184.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 216714912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714914
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 3528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714919
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714920
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714921
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714922
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714923
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714930
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714931
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714933
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714934
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714935
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714936
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714943
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714944
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714945
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714946
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714951
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714953
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714954
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714962
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714963
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714973
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714977
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 216714980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.5832.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 216714983
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3590, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714984
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3591, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714985
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3592, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3593, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714987
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3594, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714988
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 1, 'counter': 3595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3596, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3597, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3598, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3599, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714995
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216714996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3601, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3602, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3603, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216714999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3604, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3605, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715001
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3606, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 3607, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715003
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': False, 'core_order': 1, 'counter': 3608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715004
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3610, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3611, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715008
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 3612, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715009
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715010
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715011
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715012
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3616, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715013
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3617, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715014
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3618, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715015
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715017
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715018
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3621, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715019
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3622, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715020
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 3623, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715021
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715022
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 3625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715023
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 3626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715024
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715025
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3628, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715026
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3629, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715028
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715029
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715030
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715031
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3633, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715032
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3634, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715033
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3635, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715034
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 3636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715035
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 3637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715036
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 3638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715037
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715039
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715040
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3641, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715041
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715042
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715043
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715044
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715045
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715046
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3647, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715047
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715048
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715050
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715051
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 3651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715052
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715053
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715054
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 3654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715055
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3655, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7776.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 216715056
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715057
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715058
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 3658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715059
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 3659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715061
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715062
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 3661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715063
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 3662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715064
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 3663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715065
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 3664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.7776.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7776.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7776, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715066
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 3665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715067
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715068
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 3667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715069
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715070
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715072
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715073
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715074
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715075
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715076
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715077
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715078
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 5184, 'characteristic': False, 'core_order': 1, 'counter': 3676, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715079
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 3677, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3678, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715081
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3679, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715083
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3680, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715084
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3681, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715085
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715086
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715088
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715090
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715091
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715094
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 3690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715096
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715098
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715099
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3695, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715100
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3696, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715101
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3697, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715102
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3698, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715103
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715106
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715108
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 216715109
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3703, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715110
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 3704, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.11664.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11664.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11664, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 216715111
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 11664, 'characteristic': False, 'core_order': 1, 'counter': 3705, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715112
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 7776, 'characteristic': False, 'core_order': 1, 'counter': 3706, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715113
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 5832, 'characteristic': False, 'core_order': 1, 'counter': 3707, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715114
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 3888, 'characteristic': False, 'core_order': 1, 'counter': 3708, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715115
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': False, 'core_order': 1, 'counter': 3709, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715117
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': False, 'core_order': 1, 'counter': 3710, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715118
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 3711, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715119
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 3712, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715120
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 3713, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.15552.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15552.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15552, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 216715121
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 5184, 'characteristic': False, 'core_order': 1, 'counter': 3714, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715122
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 5184, 'characteristic': False, 'core_order': 1, 'counter': 3715, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715123
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2592, 'characteristic': False, 'core_order': 1, 'counter': 3716, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715124
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 3717, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715125
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 1, 'counter': 3718, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715126
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 3719, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715128
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 3720, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715129
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 3721, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715130
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3722, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715131
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 3723, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715132
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 3724, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '46656.ir.23328.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '23328.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 23328, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 216715133
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '46656.ir', 'ambient_counter': 226, 'ambient_order': 46656, 'ambient_tex': 'C_3:S_3^4.D_6', 'central': True, 'central_factor': False, 'centralizer_order': 46656, 'characteristic': True, 'core_order': 1, 'counter': 3725, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '46656.ir.46656.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '46656.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '46656.ir', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9168954550374180198, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 46656, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_3^4.D_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D4', 'C8', 'Z', 'Phi', 'PC', 'U0', 'D4', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

  Column	Type
  ambient	text
  aut_centralizer_order	numeric
  aut_label	text
  aut_quo_index	numeric
  aut_stab_index	numeric
  aut_weyl_group	text
  aut_weyl_index	numeric
  centralizer	text
  complements	text[]
  conjugacy_class_count	numeric
  contained_in	text[]
  contains	text[]
  core	text
  coset_action_label	text
  count	numeric
  diagramx	smallint[]
  generators	numeric[]
  label	text
  mobius_quo	bigint
  mobius_sub	bigint
  normal_closure	text
  normal_contained_in	text[]
  normal_contains	text[]
  normalizer	text
  old_label	text
  projective_image	text
  quotient_action_image	text
  quotient_action_kernel	text
  quotient_action_kernel_order	numeric
  quotient_fusion	jsonb
  short_label	text
  subgroup_fusion	integer[]
  weyl_group	text

  
  
  • id: 216712104
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['46656.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '3.a1', '4.l1', '9.b1', '27.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [461482882830, 1521641624, 39957120, 39916800, 39366316080, 7, 499, 6227827207, 41051125, 41050800, 269279866800, 1481684400], 'label': '46656.ir.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712105
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.e1', '12.a1', '12.v1', '16.c1', '108.bh1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '8.e1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712106
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.i1', '6.n1'], 'contains': ['24.br1', '24.bt1', '24.bx1', '36.df1', '108.di1', '108.es1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39917299, 39366316080, 6267381127, 7, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.12.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712107
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1', '72.be1', '72.df1', '72.gk1'], 'contains': ['288.bp1', '288.cp1', '288.di1', '432.kz1', '432.lf1', '432.lg1', '432.ll1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 40323593520, 6227827207, 41091127], 'label': '46656.ir.144.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gw1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712108
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1', '72.j1', '72.dg1', '72.gl1'], 'contains': ['288.bq1', '288.cq1', '288.dj1', '432.kz1', '432.lh1', '432.lk1', '432.ln1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 6227827207, 41091127], 'label': '46656.ir.144.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gx1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712109
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1', '48.ci1', '72.dh1'], 'contains': ['288.br1', '288.cr1', '288.dk1', '432.kz1', '432.li1', '432.lj1', '432.lm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 269279866800, 6227827207, 41091127], 'label': '46656.ir.144.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '144.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gy1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712110
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1', '72.be1', '72.ei1', '72.fw1'], 'contains': ['288.bp1', '288.cw1', '288.eb1', '432.la1', '432.lp1', '432.lq1', '432.lr1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744007, 1174327, 268280812800, 325, 40323593520], 'label': '46656.ir.144.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gz1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712111
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1', '72.j1', '72.er1', '72.fv1'], 'contains': ['288.bq1', '288.cy1', '288.du1', '432.la1', '432.ls1', '432.lt1', '432.lu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 325, 1481684400, 1481684504], 'label': '46656.ir.144.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ha1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712112
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cg1', '72.q1', '72.fx1', '72.go1'], 'contains': ['288.bt1', '288.cd1', '288.ci1', '432.lb1', '432.lc1', '432.lv1', '432.lw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684835, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.144.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hb1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216712113
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1', '72.t1', '72.fu1', '72.gk1'], 'contains': ['288.by1', '288.cf1', '288.cp1', '432.ld1', '432.le1', '432.lw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 39916807, 268280812800, 325, 40323593520, 6227827207], 'label': '46656.ir.144.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hc1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712114
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ch1', '72.bf1'], 'contains': ['288.bs1', '288.ch1', '288.de1', '432.lg1', '432.lj1', '432.lk1', '432.lx1', '432.ly1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684725, 39366316080, 268280812800, 6227827207, 104, 41091127], 'label': '46656.ir.144.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '144.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hd1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216712115
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ch1', '48.ck1', '72.bg1', '72.cs1', '72.go1'], 'contains': ['288.bt1', '288.ci1', '288.dg1', '432.lf1', '432.lh1', '432.li1', '432.lx1', '432.ly1', '432.lz1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 269279866800, 6227827207, 41091127], 'label': '46656.ir.144.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.he1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 216712116
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ch1', '72.bh1', '72.cz1', '72.gk1'], 'contains': ['288.by1', '288.cj1', '288.di1', '432.ll1', '432.lm1', '432.ln1', '432.lx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 6227827207, 104, 41091127], 'label': '46656.ir.144.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hf1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712117
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.h1', '6.n1'], 'contains': ['24.bs1', '24.bt1', '24.bw1', '36.dg1', '108.dj1', '108.er1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 40819, 7, 269279866800], 'label': '46656.ir.12.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712118
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ci1', '48.ck1', '72.cu1'], 'contains': ['288.bu1', '288.cm1', '288.cz1', '432.li1', '432.ma1', '432.mb1', '432.mc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593624, 132379435521, 40323593520, 269279866800, 6227827207, 41091127], 'label': '46656.ir.144.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '144.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hg1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216712119
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ci1'], 'contains': ['288.bw1', '288.co1', '288.da1', '432.lj1', '432.ma1', '432.mc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [300933848880, 270715783064, 325, 438010715790, 6227827207, 41091127], 'label': '46656.ir.144.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hh1', 'old_label': '144.hh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hh1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216712120
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ci1', '72.de1'], 'contains': ['288.bz1', '288.cs1', '288.db1', '432.lm1', '432.lo1', '432.ma1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [300933848880, 325, 382729979624, 457175461950, 6227827207, 41091127], 'label': '46656.ir.144.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.hi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hi1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712121
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cj1', '72.bf1'], 'contains': ['288.bs1', '288.ct1', '288.dl1', '432.lq1', '432.lt1', '432.md1', '432.me1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 1481684725, 1174327, 39366316080, 268280812800, 104], 'label': '46656.ir.144.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '144.hj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hj1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216712122
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cj1', '72.bg1', '72.cv1', '72.fx1'], 'contains': ['288.bt1', '288.cv1', '288.dn1', '432.lp1', '432.ls1', '432.md1', '432.me1', '432.mf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 1481684835, 1481684400, 269279866800], 'label': '46656.ir.144.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.hk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hk1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 216712123
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cj1', '72.bh1', '72.ei1', '72.fu1'], 'contains': ['288.by1', '288.cw1', '288.dt1', '432.lr1', '432.lu1', '432.md1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 268280812800, 325, 104], 'label': '46656.ir.144.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.hl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hl1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712124
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ds1', '48.ck1', '72.ck1'], 'contains': ['288.cb1', '288.ck1', '288.dc1', '432.lz1', '432.mb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 624302466480, 1481684400, 269279866800, 6227827207, 41091127], 'label': '46656.ir.144.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.hm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hm1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712125
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1', '72.p1', '72.fa1', '72.gj1'], 'contains': ['288.cy1', '1296.lu1', '1296.lw1', '1296.ly1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1174327, 39366316080, 325, 1481684400, 1481684504, 6227752218], 'label': '46656.ir.144.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '144.hn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.hn1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
  • id: 216712126
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1', '72.p1', '72.fb1', '72.gj1'], 'contains': ['288.cy1', '1296.lv1', '1296.lx1', '1296.lz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1174327, 39366316080, 6267669018, 325, 1481684400, 1481684504], 'label': '46656.ir.144.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '144.ho1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ho1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
  • id: 216712127
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '54.f1', '81.b1'], 'contains': ['324.a1', '324.b1', '324.c1', '324.d1', '324.g1', '324.cx1', '324.cy1', '324.dc1', '324.dd1', '324.dj1', '324.dk1', '486.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 499, 1481684400, 443130957804, 269279866800, 40320, 1481684844], 'label': '46656.ir.162.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712128
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.i1', '6.m1'], 'contains': ['24.bt1', '24.bu1', '24.bv1', '36.dh1', '108.dk1', '108.et1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 7, 39957619, 269279866800], 'label': '46656.ir.12.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712184
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.w1', '108.c1', '108.e1', '108.j1'], 'contains': ['432.d1', '432.fd1', '432.fe1', '648.m1', '1944.i1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 499, 7, 325, 39916800, 104], 'label': '46656.ir.216.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712129
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '54.g1', '81.b1'], 'contains': ['324.c1', '324.f1', '324.h1', '324.de1', '324.df1', '324.dl1', '324.dm1', '1458.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 1481684400, 443130957804, 269279866800, 40320, 39957619, 1481684844], 'label': '46656.ir.162.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712130
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '54.h1', '81.b1'], 'contains': ['324.d1', '324.e1', '324.h1', '324.dn1', '324.do1', '324.dp1', '324.ds1', '1458.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 499, 1481684400, 269279866800, 443609999724, 40320, 1481684844], 'label': '46656.ir.162.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712131
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '54.i1', '81.b1'], 'contains': ['324.e1', '324.f1', '324.g1', '324.dq1', '324.dr1', '324.dt1', '324.du1', '1458.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 1481684400, 269279866800, 443609999724, 40320, 39957619, 1481684844], 'label': '46656.ir.162.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712132
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.j1', '81.a1'], 'contains': ['324.j1', '324.k1', '324.l1', '324.m1', '324.p1', '324.ee1', '324.ef1', '324.eg1', '324.eh1', '324.el1', '324.em1', '1458.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 6227827207, 499, 7, 104], 'label': '46656.ir.162.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712133
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '54.k1', '81.a1'], 'contains': ['324.l1', '324.o1', '324.q1', '324.ei1', '324.ej1', '324.en1', '324.eo1', '1458.b1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 6227827207, 7, 39957619, 104], 'label': '46656.ir.162.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712134
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '54.o1', '81.a1'], 'contains': ['324.m1', '324.n1', '324.q1', '324.ep1', '324.eq1', '324.er1', '324.eu1', '1458.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 6267381127, 499, 7, 104], 'label': '46656.ir.162.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712135
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '54.p1', '81.a1'], 'contains': ['324.n1', '324.o1', '324.p1', '324.es1', '324.et1', '324.ev1', '324.ew1', '1458.d1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 6267381127, 7, 39957619, 104], 'label': '46656.ir.162.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712136
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '54.b1', '81.a1'], 'contains': ['324.x1', '324.z1', '324.bb1', '324.eg1', '324.ei1', '324.ep1', '324.es1', '1458.e1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 499, 7, 104, 40320], 'label': '46656.ir.162.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '162.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712137
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '54.c1', '81.a1'], 'contains': ['324.x1', '324.ba1', '324.bc1', '324.eh1', '324.ej1', '324.er1', '324.et1', '1458.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 7, 39957619, 104, 40320], 'label': '46656.ir.162.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712138
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '54.d1', '81.a1'], 'contains': ['324.y1', '324.z1', '324.bc1', '324.el1', '324.en1', '324.eq1', '324.ev1', '1458.g1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6267381127, 499, 7, 104, 40320], 'label': '46656.ir.162.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.k1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712139
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.k1', '6.o1', '6.p1'], 'contains': ['24.c1', '24.bo1', '24.bq1', '24.cp1', '24.cv1', '24.cw1', '24.de1', '36.ce1', '36.di1', '108.fb1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.12.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712140
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '54.e1', '81.a1'], 'contains': ['324.y1', '324.ba1', '324.bb1', '324.em1', '324.eo1', '324.eu1', '324.ew1', '1458.h1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6267381127, 7, 39957619, 104, 40320], 'label': '46656.ir.162.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.l1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712141
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '54.f1'], 'contains': ['324.bi1', '324.bj1', '324.bk1', '324.bl1', '324.bm1', '324.bn1', '324.bo1', '324.cs1', '324.ct1', '324.cv1', '324.cw1', '324.da1', '324.db1', '324.dh1', '324.di1', '486.a1', '486.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41050800, 499, 443130957804, 269279866800, 40320, 37885034880], 'label': '46656.ir.162.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '162.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.m1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712142
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.j1', '54.l1'], 'contains': ['324.bs1', '324.bx1', '324.by1', '324.eb1', '324.ec1', '324.fe1', '324.fh1', '486.h1', '486.m1', '648.gq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [7, 2957880565, 655807627898, 39916800, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.162.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '162.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216712143
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '54.l1', '54.q1', '81.a1'], 'contains': ['324.l1', '324.n1', '324.r1', '324.t1', '324.x1', '324.y1', '324.bf1', '324.bg1', '324.bu1', '324.bv1', '324.ca1', '324.ek1', '324.ex1', '324.fc1', '324.fg1', '486.m1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 7, 41051125, 39957224, 39916800, 6227827207], 'label': '46656.ir.162.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712144
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.m1', '54.r1', '81.a1'], 'contains': ['324.m1', '324.o1', '324.z1', '324.ba1', '324.bu1', '324.ey1', '324.ez1', '1458.j1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 39916800, 499, 7, 41051125], 'label': '46656.ir.162.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.p1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712145
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1', '54.n1', '54.s1', '81.a1'], 'contains': ['324.p1', '324.q1', '324.bb1', '324.bc1', '324.bu1', '324.fa1', '324.fb1', '1458.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 39916800, 7, 41051125, 6227827818], 'label': '46656.ir.162.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.q1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712146
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.p1', '54.q1'], 'contains': ['324.v1', '324.w1', '324.bd1', '324.bh1', '324.br1', '324.bt1', '324.bw1', '324.cb1', '324.ce1', '324.cf1', '324.cg1', '324.ea1', '324.ed1', '324.fd1', '324.fi1', '486.m1', '486.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355459144755, 268280812800, 39957120, 41050800, 7, 39916800, 6227827207], 'label': '46656.ir.162.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '162.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.r1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712147
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '54.t1', '81.b1'], 'contains': ['324.ch1', '324.cj1', '324.cl1', '324.dc1', '324.de1', '324.dn1', '324.dq1', '1458.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050800, 499, 1481684400, 443130957804, 39916800, 269279866800, 1481684844], 'label': '46656.ir.162.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '162.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.s1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712148
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '54.u1', '81.b1'], 'contains': ['324.ch1', '324.ck1', '324.cm1', '324.dd1', '324.df1', '324.dp1', '324.dr1', '1458.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 1481684400, 443130957804, 39916800, 269279866800, 39957619, 1481684844], 'label': '46656.ir.162.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.t1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712149
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '54.v1', '81.b1'], 'contains': ['324.ci1', '324.cj1', '324.cm1', '324.dj1', '324.dl1', '324.do1', '324.dt1', '1458.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 499, 1481684400, 39916800, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.162.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.u1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712150
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '6.l1', '6.m1', '6.p1'], 'contains': ['24.c1', '24.bu1', '24.by1', '36.dl1', '108.do1', '108.fe1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 7, 41051125, 6227827818, 269279866800, 1521641624], 'label': '46656.ir.12.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712151
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '54.w1', '81.b1'], 'contains': ['324.ci1', '324.ck1', '324.cl1', '324.dk1', '324.dm1', '324.ds1', '324.du1', '1458.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 1481684400, 39916800, 269279866800, 443609999724, 39957619, 1481684844], 'label': '46656.ir.162.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.v1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712152
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.x1', '54.y1', '81.b1'], 'contains': ['324.c1', '324.e1', '324.s1', '324.u1', '324.ch1', '324.ci1', '324.cn1', '324.co1', '324.cp1', '324.cq1', '324.cr1', '324.dg1', '324.dv1', '324.ff1', '324.fj1', '1458.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 7, 1481684400, 39916800, 6227827207], 'label': '46656.ir.162.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.w1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712153
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '54.z1', '81.b1'], 'contains': ['324.d1', '324.f1', '324.bp1', '324.bq1', '324.cc1', '324.cd1', '324.cj1', '324.ck1', '324.cp1', '324.dw1', '324.dx1', '486.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 41050800, 499, 39916800, 37885034880], 'label': '46656.ir.162.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.x1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712154
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1', '54.ba1', '81.b1'], 'contains': ['324.g1', '324.h1', '324.cl1', '324.cm1', '324.cp1', '324.dy1', '324.dz1', '1458.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 1481684400, 39957120, 39916800, 6227827818], 'label': '46656.ir.162.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.y1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712155
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.u1', '54.bb1', '81.b1'], 'contains': ['324.dc1', '324.df1', '324.dg1', '324.do1', '324.du1', '324.dw1', '324.dy1', '1458.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 499, 1481684400, 1521641964, 269279866800, 443609999724], 'label': '46656.ir.162.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.z1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712156
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.v1', '54.bc1', '81.b1'], 'contains': ['324.dd1', '324.de1', '324.dg1', '324.ds1', '324.dt1', '324.dx1', '324.dz1', '1458.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39917299, 39957120, 41050800, 1481684400, 1521641964, 269279866800, 443609999724], 'label': '46656.ir.162.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.ba1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712157
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.w1', '54.bd1', '81.b1'], 'contains': ['324.dj1', '324.dm1', '324.dn1', '324.dr1', '324.dv1', '324.dw1', '324.dz1', '1458.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1521641657, 6267744007, 39366316080, 39957120, 41050800, 7, 1481684400], 'label': '46656.ir.162.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bb1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712158
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.x1', '54.be1', '81.b1'], 'contains': ['324.dk1', '324.dl1', '324.dp1', '324.dq1', '324.dv1', '324.dx1', '324.dy1', '1458.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [43633820302, 6267744007, 39366316080, 39957120, 41050800, 7, 1481684400], 'label': '46656.ir.162.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bc1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712159
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.u1', '54.bf1', '54.bh1', '81.a1'], 'contains': ['324.eg1', '324.ej1', '324.ek1', '324.eq1', '324.ew1', '324.ey1', '324.fa1', '1458.l1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 6227827207, 499, 7, 41051125], 'label': '46656.ir.162.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bd1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712160
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.v1', '54.bg1', '54.bi1', '81.a1'], 'contains': ['324.eh1', '324.ei1', '324.ek1', '324.eu1', '324.ev1', '324.ez1', '324.fb1', '1458.m1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39917299, 39957120, 41050800, 7, 41051125, 39957224, 6227827207], 'label': '46656.ir.162.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.be1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712161
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1', '6.l1', '6.n1', '6.o1'], 'contains': ['24.c1', '24.bw1', '24.bx1', '36.dm1', '108.dp1', '108.ff1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6267744618, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.12.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712162
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.w1', '54.bj1', '54.bl1', '81.a1'], 'contains': ['324.el1', '324.eo1', '324.ep1', '324.et1', '324.ex1', '324.ey1', '324.fb1', '1458.n1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957224, 6267744007, 41050800, 39957120, 499, 7, 41051125], 'label': '46656.ir.162.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bf1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712163
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '162.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.x1', '54.bk1', '54.bm1', '81.a1'], 'contains': ['324.em1', '324.en1', '324.er1', '324.es1', '324.ex1', '324.ez1', '324.fa1', '1458.o1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 7, 41051125, 39957224, 6227827818], 'label': '46656.ir.162.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bg1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712164
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': ['243.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '96.a1', '96.b1', '96.c1', '96.d1', '96.h1', '96.o1', '96.p1', '96.t1', '96.w1', '96.y1', '96.bg1'], 'contains': ['576.a1', '576.b1', '576.c1', '576.d1', '576.k1', '576.l1', '576.m1'], 'core': '192.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.192.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': ['48.d1', '96.a1', '96.b1', '96.c1'], 'normal_contains': ['1728.a1', '5184.a1'], 'normalizer': '1.a1', 'old_label': '192.a1', 'projective_image': '46656.ir', 'quotient_action_image': '192.1469', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '192.1469'}
  • id: 216712165
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ce1', '64.a1', '96.e1', '96.i1', '96.m1', '96.s1', '96.u1', '96.z1', '96.bc1'], 'contains': ['576.c1', '576.e1', '576.g1', '576.p1', '576.q1', '576.r1', '576.s1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [39366316080, 622713012218, 325, 1481684400, 269279866800], 'label': '46656.ir.192.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '192.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216712166
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cf1', '64.a1', '96.n1', '96.v1', '96.bd1'], 'contains': ['576.c1', '576.f1', '576.h1', '576.q1', '576.t1', '576.t2'], 'core': '1728.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [39366316080, 461333739315, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.192.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1', 'old_label': '192.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712167
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '96.j1', '96.ba1', '96.be1'], 'contains': ['576.d1', '576.e1', '576.h1', '576.r1', '576.t1', '576.t2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [270715782960, 40323593520, 31658054504, 34096648645, 461482882830], 'label': '46656.ir.192.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '192.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712168
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '96.bf1'], 'contains': ['576.d1', '576.f1', '576.g1', '576.h1', '576.s1', '576.t1', '576.t2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [40323593624, 270715782960, 40323593520, 34096648645, 461482882830], 'label': '46656.ir.192.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '192.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216712169
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '96.f1', '96.k1', '96.l1', '96.q1', '96.x1', '96.bb1', '96.bh1'], 'contains': ['576.e1', '576.f1', '576.i1', '576.m1', '576.n1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [40323593624, 325, 270715782960, 40323593520, 461482882830], 'label': '46656.ir.192.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '192.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216712170
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '96.g1', '96.r1', '96.bi1'], 'contains': ['576.g1', '576.h1', '576.j1', '576.m1', '576.o1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [40323593624, 195088320270, 325, 270715782960, 40323593520], 'label': '46656.ir.192.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '192.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1', 'subgroup_fusion': None, 'weyl_group': '216.67'}
  • id: 216712171
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['216.gd1', '216.ic1', '216.id1', '216.ge1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.ci1', '72.cj1', '108.co1', '108.cp1', '108.cq1'], 'contains': ['432.a1', '432.bm1', '432.cn1', '648.dq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800], 'label': '46656.ir.216.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': ['24.a1', '72.a1'], 'normal_contains': ['432.a1', '864.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '46656.ir', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.9', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712172
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1', '6.k1'], 'contains': ['24.d1', '24.ch1', '24.ci1', '24.ck1', '24.cr1', '24.ct1', '24.de1', '36.dn1', '36.do1', '108.fg1'], 'core': '24.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 6227827200, 1521641624], 'label': '46656.ir.12.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712173
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.d1', '72.q1', '108.a1'], 'contains': ['432.b1', '432.f1', '432.p1', '432.dk1', '432.dv1', '432.gq1', '432.lb1', '648.a1', '648.g1', '648.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 1481684504, 39916800, 6227827207], 'label': '46656.ir.216.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '216.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712174
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.r1', '108.a1', '108.b1', '108.cl1'], 'contains': ['432.b1', '432.k1', '432.u1', '432.dp1', '432.dt1', '432.ij1', '432.ka1', '648.b1', '648.i1', '648.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 1134000, 31697930984, 37885034880], 'label': '46656.ir.216.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712175
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.s1', '108.c1', '108.d1', '108.g1'], 'contains': ['432.d1', '432.e1', '432.r1', '432.ec1', '432.em1', '432.fv1', '432.ky1', '648.g1', '648.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 7, 325, 39916800, 6227827207, 104], 'label': '46656.ir.216.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712176
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.t1', '108.e1', '108.f1', '108.g1'], 'contains': ['432.d1', '432.h1', '432.s1', '432.ed1', '432.ep1', '432.gv1', '432.ld1', '648.h1', '648.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 7, 325, 39916800, 40323593520, 6227827207], 'label': '46656.ir.216.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712177
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1', '72.v1', '108.h1', '108.i1', '108.bv1'], 'contains': ['432.c1', '432.i1', '432.w1', '432.eg1', '432.ek1', '432.ia1', '432.jk1', '648.i1', '648.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 7, 325, 1134000, 31697930984, 37885034880], 'label': '46656.ir.216.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712178
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1', '72.u1', '108.g1', '108.j1', '108.k1'], 'contains': ['432.d1', '432.j1', '432.x1', '432.ei1', '432.el1', '432.ib1', '432.jl1', '648.j1', '648.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 39957120, 7, 325, 39957224, 1134000], 'label': '46656.ir.216.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712179
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.ba1', '108.h1', '108.p1', '108.bt1'], 'contains': ['432.c1', '432.er1', '432.es1', '648.m1', '1944.e1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [499, 7, 325, 39916800, 31658054504, 37885034880], 'label': '46656.ir.216.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '216.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712180
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.bb1', '108.i1', '108.p1', '108.bu1'], 'contains': ['432.c1', '432.es1', '432.ew1', '648.n1', '1944.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1481684504, 1481684400, 7, 39957619, 325, 40320], 'label': '46656.ir.216.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712181
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.bc1', '108.i1', '108.q1', '108.bt1'], 'contains': ['432.c1', '432.et1', '432.ex1', '648.n1', '1944.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 7, 325, 355419187304, 40320, 39957619], 'label': '46656.ir.216.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '216.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712182
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1', '72.bd1', '108.h1', '108.q1', '108.bu1'], 'contains': ['432.c1', '432.ev1', '432.ex1', '648.p1', '1944.h1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134000, 31658054504, 37885034880, 7, 39957619, 325], 'label': '46656.ir.216.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712183
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.j1', '6.j1'], 'contains': ['24.cl1', '24.cy1', '24.dc1', '36.do1', '36.dp1', '48.bm1', '324.fe1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [624190336641, 39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827200, 1521641624], 'label': '46656.ir.12.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216712185
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.x1', '108.c1', '108.f1', '108.k1'], 'contains': ['432.d1', '432.ff1', '432.fj1', '648.o1', '1944.j1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 7, 325, 39916800, 6227827818, 104], 'label': '46656.ir.216.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712186
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '72.y1', '108.d1', '108.e1', '108.k1'], 'contains': ['432.d1', '432.fg1', '432.fk1', '648.o1', '1944.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 40323593520, 39916800, 7, 6227827818, 325], 'label': '46656.ir.216.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712187
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1', '72.z1', '108.d1', '108.f1', '108.j1'], 'contains': ['432.d1', '432.fh1', '432.fi1', '648.p1', '1944.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 7, 325, 1134000, 39957619, 104], 'label': '46656.ir.216.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712188
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1', '72.be1', '108.g1'], 'contains': ['432.e1', '432.s1', '432.x1', '432.ga1', '432.gh1', '432.kz1', '432.la1', '648.q1', '648.r1', '648.s1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 1174327, 325, 39916800, 40323593520, 6227827207], 'label': '46656.ir.216.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712189
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '72.bg1', '108.a1'], 'contains': ['432.f1', '432.p1', '432.u1', '432.gz1', '432.hg1', '432.lh1', '432.ls1', '648.q1', '648.u1', '648.v1', '648.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684835, 1481684400, 39916800, 6227827207], 'label': '46656.ir.216.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '216.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712190
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.j1', '72.bf1'], 'contains': ['432.g1', '432.q1', '432.v1', '432.ha1', '432.hj1', '432.lk1', '432.lt1', '648.r1', '648.u1', '648.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1481684725, 1174327, 39366316080, 39916800, 6227827207, 104], 'label': '46656.ir.216.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '216.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712191
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1', '72.bh1', '108.g1'], 'contains': ['432.h1', '432.r1', '432.x1', '432.hb1', '432.hl1', '432.ln1', '432.lu1', '648.s1', '648.u1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 39366316080, 325, 39916800, 6227827207, 104], 'label': '46656.ir.216.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712192
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1', '72.bi1', '108.g1'], 'contains': ['432.e1', '432.h1', '432.j1', '432.fr1', '432.gk1', '432.ht1', '432.je1', '648.t1', '648.x1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174320, 39916800, 6227827200, 104, 1174645], 'label': '46656.ir.216.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712193
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.k1', '72.bj1', '108.a1', '108.l1', '108.cm1'], 'contains': ['432.f1', '432.k1', '432.gn1', '432.hu1', '432.jy1', '648.x1', '648.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 39916800, 6227827200], 'label': '46656.ir.216.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '216.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712194
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1', '6.k1'], 'contains': ['24.d1', '24.cn1', '24.co1', '24.cq1', '24.cs1', '24.cw1', '24.db1', '36.dq1', '36.dr1', '108.fl1'], 'core': '24.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 6227827207, 1521641624], 'label': '46656.ir.12.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712195
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1', '72.bk1', '108.bv1'], 'contains': ['432.i1', '432.n1', '432.o1', '432.ia1', '432.ic1', '432.jn1', '432.js1', '648.z1', '648.bd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41050807, 39957120, 325, 1134000, 31697930984, 37885034880], 'label': '46656.ir.216.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712196
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1', '72.bl1', '108.g1'], 'contains': ['432.j1', '432.r1', '432.s1', '432.ih1', '432.ii1', '432.jp1', '432.jv1', '648.ba1', '648.be1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174320, 39916800, 6227827207, 104, 1174645], 'label': '46656.ir.216.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712197
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.l1', '72.bm1', '108.l1', '108.m1', '108.cl1'], 'contains': ['432.k1', '432.m1', '432.il1', '432.ke1', '432.kh1', '648.bd1', '648.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 1134000, 31697930984, 37885034880], 'label': '46656.ir.216.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712198
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.m1', '72.bn1', '108.a1', '108.m1', '108.cn1'], 'contains': ['432.k1', '432.p1', '432.io1', '432.kg1', '432.kk1', '648.be1', '648.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 39916800, 6227827207], 'label': '46656.ir.216.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712199
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.n1', '72.bo1', '108.b1', '108.m1', '108.cm1'], 'contains': ['432.k1', '432.kn1', '432.ko1', '648.bh1', '1944.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267381120, 39366316080, 1481684835, 1174320, 1481684400, 39916800], 'label': '46656.ir.216.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '216.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712200
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '72.bp1', '108.b1', '108.l1', '108.cn1'], 'contains': ['432.k1', '432.kp1', '432.kq1', '648.bi1', '1944.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 6267381127, 1481684835, 1174320, 1481684400, 39916800], 'label': '46656.ir.216.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712201
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1', '108.n1', '108.o1', '108.p1', '108.q1', '108.r1', '108.s1', '108.bv1'], 'contains': ['432.c1', '432.n1', '432.y1', '432.ej1', '432.iv1', '648.bm1', '648.bn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 7, 325, 1481684400, 39916800, 1521641624], 'label': '46656.ir.216.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712202
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '108.n1', '108.t1', '108.bw1'], 'contains': ['432.y1', '432.gi1', '432.ja1', '648.bo1', '648.bp1', '648.bq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 6227827200, 355419187304, 40320, 1174645], 'label': '46656.ir.216.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1', 'subgroup_fusion': None, 'weyl_group': '32.45'}
  • id: 216712203
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1', '108.o1', '108.u1', '108.bw1'], 'contains': ['432.y1', '432.iu1', '432.jb1', '648.br1', '648.bs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 268280812800, 1174320, 355419187304, 40320, 1174645], 'label': '46656.ir.216.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 216712204
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1', '108.t1', '108.u1', '108.bv1'], 'contains': ['432.o1', '432.w1', '432.y1', '432.iw1', '432.iy1', '648.bt1', '648.bu1', '648.bv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050807, 39957120, 325, 1481684400, 39916800, 1521641624], 'label': '46656.ir.216.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712205
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.k1', '6.j1'], 'contains': ['24.cx1', '24.cy1', '24.cz1', '36.dr1', '36.ds1', '48.ck1', '324.fh1'], 'core': '72.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 622713012218, 6227827207, 41051125, 39916807, 269279866800], 'label': '46656.ir.12.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216712206
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1', '108.n1', '108.u1', '108.bx1'], 'contains': ['432.y1', '432.ix1', '432.jc1', '648.bw1', '648.bx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 355419187304, 40320, 6227827207, 1174645], 'label': '46656.ir.216.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216712207
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1', '108.o1', '108.t1', '108.bx1'], 'contains': ['432.y1', '432.iz1', '432.jd1', '648.by1', '648.bz1', '648.ca1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 355419187304, 40320, 1174645], 'label': '46656.ir.216.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712208
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1', '108.v1', '108.w1', '108.x1'], 'contains': ['432.z1', '432.bi1', '432.bv1', '432.co1', '432.ct1', '432.gs1', '432.lv1', '648.a1', '648.cb1', '648.cc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.216.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712209
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1', '108.x1', '108.y1', '108.z1', '108.ba1', '108.bb1', '108.bc1', '108.co1'], 'contains': ['432.z1', '432.bm1', '432.ch1', '432.cr1', '432.cs1', '432.is1', '432.kc1', '648.b1', '648.cd1', '648.ce1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 269279866800, 1134000], 'label': '46656.ir.216.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712210
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.do1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '108.v1', '108.y1', '108.ca1'], 'contains': ['432.z1', '432.cw1', '432.cx1', '648.c1', '648.cf1', '648.cj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 499, 1481684400, 39916800, 269279866800, 1481684844], 'label': '46656.ir.216.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216712211
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '108.ba1', '108.ca1', '108.cb1'], 'contains': ['432.z1', '432.cx1', '432.da1', '648.d1', '648.ck1', '648.cl1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 40320, 39957619, 1481684844], 'label': '46656.ir.216.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '216.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bk1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712212
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '108.v1', '108.w1', '108.bb1'], 'contains': ['432.z1', '432.cy1', '432.db1', '648.e1', '648.cg1', '648.ch1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 39916800, 6227827818, 269279866800], 'label': '46656.ir.216.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712213
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '108.w1', '108.y1', '108.cb1'], 'contains': ['432.z1', '432.cz1', '432.da1', '648.f1', '648.ci1', '648.cm1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 1134000, 39957619, 1481684844], 'label': '46656.ir.216.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bm1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712214
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.q1', '72.s1', '108.bd1'], 'contains': ['432.ba1', '432.bd1', '432.bt1', '432.di1', '432.du1', '432.ft1', '432.lc1', '648.g1', '648.cb1', '648.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 39916800, 6227827207, 104], 'label': '46656.ir.216.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712215
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.q1', '72.t1', '108.bd1'], 'contains': ['432.ba1', '432.bg1', '432.bw1', '432.dj1', '432.dx1', '432.gt1', '432.lw1', '648.h1', '648.cc1', '648.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [268280812800, 7, 39916800, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.216.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '216.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bo1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712216
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['11664.bn1', '11664.q1', '11664.n1', '11664.bm1', '11664.l1', '11664.o1', '11664.m1', '11664.p1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.c1', '8.d1', '12.w1', '12.x1', '16.i1', '108.bo1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 6227827200, 41050800, 1481684400, 39957120, 39916800, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '8.c1', '8.d1', '36.a1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '46656.ir', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216712217
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['2916.a1', '2916.b1', '2916.v1', '2916.w1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1'], 'contains': ['48.d1', '48.ce1', '48.cf1', '64.a1', '432.jw1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.16.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1'], 'normal_contains': ['48.d1', '144.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '46656.ir', 'quotient_action_image': '16.10', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216712218
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.r1', '72.u1', '108.bd1'], 'contains': ['432.ba1', '432.bk1', '432.bz1', '432.do1', '432.dr1', '432.ik1', '432.jg1', '648.j1', '648.cd1', '648.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [301891126320, 39957120, 7, 1481684400, 1134000, 1521641624], 'label': '46656.ir.216.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712219
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.r1', '72.v1', '108.cl1'], 'contains': ['432.bb1', '432.bl1', '432.cc1', '432.dp1', '432.ds1', '432.il1', '432.ji1', '648.i1', '648.ce1', '648.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 1134000, 1521641624], 'label': '46656.ir.216.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '216.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712220
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1', '72.t1', '108.be1', '108.bf1', '108.bg1'], 'contains': ['432.bc1', '432.bf1', '432.by1', '432.ea1', '432.en1', '432.fw1', '432.le1', '648.k1', '648.cn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 7, 325, 39916800, 355419187304, 6227827207], 'label': '46656.ir.216.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712240
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '108.bj1', '108.br1', '108.bw1'], 'contains': ['432.bj1', '432.ja1', '432.jb1', '648.bb1', '648.da1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 268280812800, 1174320, 39916800, 355419187304, 1174645], 'label': '46656.ir.216.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cj1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712221
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1', '72.v1', '108.bg1', '108.bi1', '108.bj1', '108.bk1', '108.bl1', '108.bm1', '108.bv1'], 'contains': ['432.bc1', '432.bj1', '432.cd1', '432.eg1', '432.ej1', '432.ic1', '432.iw1', '648.l1', '648.co1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 7, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.216.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712222
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '72.ba1', '108.be1', '108.bi1', '108.bt1'], 'contains': ['432.bc1', '432.er1', '432.et1', '648.m1', '1944.br1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 499, 7, 325, 39916800, 355419187304], 'label': '46656.ir.216.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712223
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '72.bc1', '108.bk1', '108.bt1', '108.bu1'], 'contains': ['432.bc1', '432.es1', '432.ex1', '648.n1', '1944.bs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [31658054504, 37885034880, 7, 39957619, 325, 40320], 'label': '46656.ir.216.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '216.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712224
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1', '72.y1', '108.be1', '108.bf1', '108.bl1'], 'contains': ['432.bc1', '432.eu1', '432.ey1', '648.o1', '1944.bt1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 7, 325, 39916800, 6227827818, 355419187304], 'label': '46656.ir.216.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712225
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '72.bd1', '108.bf1', '108.bi1', '108.bu1'], 'contains': ['432.bc1', '432.ev1', '432.ew1', '648.p1', '1944.bu1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 325, 1481684400, 1481684504, 1134000, 39957619], 'label': '46656.ir.216.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712226
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.be1', '72.bg1', '108.bd1'], 'contains': ['432.bd1', '432.bw1', '432.bz1', '432.fx1', '432.gb1', '432.lf1', '432.lp1', '648.q1', '648.cp1', '648.cq1', '648.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40323593624, 1174327, 268280812800, 39916800, 40323593520, 6227827207], 'label': '46656.ir.216.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bx1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712227
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.be1', '72.bf1'], 'contains': ['432.be1', '432.bx1', '432.ca1', '432.fy1', '432.gc1', '432.lg1', '432.lq1', '648.r1', '648.cp1', '648.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1174327, 268280812800, 294706903784, 301891126645, 39916800, 6227827207], 'label': '46656.ir.216.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '216.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712228
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '8.h1', '8.i1', '8.j1'], 'contains': ['32.a1', '32.b1', '32.e1', '48.l1', '48.o1', '48.p1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6227827207, 7, 325, 269279866800, 461482882830], 'label': '46656.ir.16.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216712229
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.be1', '72.bh1', '108.bg1'], 'contains': ['432.bf1', '432.by1', '432.cd1', '432.fz1', '432.gf1', '432.ll1', '432.lr1', '648.s1', '648.cp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 268280812800, 325, 39916800, 355419187304, 6227827207], 'label': '46656.ir.216.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bz1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712230
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bi1', '108.bg1', '108.bn1', '108.bw1'], 'contains': ['432.bf1', '432.bj1', '432.fp1', '432.gi1', '432.iu1', '648.t1', '648.cs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 6227827200, 355419187304, 1174645], 'label': '46656.ir.216.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ca1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712231
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bf1', '72.bg1', '72.bh1', '108.bd1'], 'contains': ['432.bg1', '432.bt1', '432.bz1', '432.gw1', '432.hf1', '432.lx1', '432.md1', '648.u1', '648.cp1', '648.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1174327, 39366316080, 268280812800, 39916800, 6227827207, 104], 'label': '46656.ir.216.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712232
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bf1', '72.bg1'], 'contains': ['432.bh1', '432.bu1', '432.ce1', '432.gx1', '432.hm1', '432.ly1', '432.me1', '648.w1', '648.cr1', '648.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1174327, 39366316080, 268280812800, 1481684504, 39916800, 6227827207], 'label': '46656.ir.216.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '216.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cc1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712233
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bg1', '108.x1'], 'contains': ['432.bi1', '432.bv1', '432.ch1', '432.gy1', '432.ho1', '432.lz1', '432.mf1', '648.v1', '648.cq1', '648.ct1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.216.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cd1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712234
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bi1', '72.bj1', '108.bd1'], 'contains': ['432.bd1', '432.bg1', '432.bk1', '432.fs1', '432.gm1', '432.hr1', '432.jf1', '648.x1', '648.cs1', '648.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 39916800, 6227827200, 104], 'label': '46656.ir.216.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '216.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712235
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bj1', '108.x1', '108.bp1', '108.cp1'], 'contains': ['432.bi1', '432.bm1', '432.gp1', '432.hw1', '432.jz1', '648.y1', '648.cu1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 39916800, 269279866800, 6227827200], 'label': '46656.ir.216.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cf1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712236
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '108.bh1', '108.bo1', '108.bq1'], 'contains': ['432.jw1', '648.cv1', '648.cw1', '648.cx1', '864.by1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 174452060430, 39916800], 'label': '46656.ir.216.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cg1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 216712237
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bk1', '108.bn1', '108.br1', '108.bv1'], 'contains': ['432.bj1', '432.bs1', '432.ia1', '432.iv1', '432.iy1', '648.z1', '648.cy1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050807, 39957120, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.216.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ch1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712238
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bl1', '108.bg1', '108.br1', '108.bx1'], 'contains': ['432.bj1', '432.by1', '432.if1', '432.ix1', '432.iz1', '648.ba1', '648.cz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 355419187304, 6227827207, 1174645], 'label': '46656.ir.216.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ci1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712239
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '8.h1', '8.k1', '8.l1'], 'contains': ['32.a1', '32.c1', '32.f1', '48.a1', '48.m1', '48.q1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 461482882830], 'label': '46656.ir.16.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216712241
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '108.bj1', '108.bn1', '108.bx1'], 'contains': ['432.bj1', '432.jc1', '432.jd1', '648.bc1', '648.db1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 39916800, 355419187304, 1174645], 'label': '46656.ir.216.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ck1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712242
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bk1', '72.bm1', '108.cl1'], 'contains': ['432.bl1', '432.bn1', '432.br1', '432.ij1', '432.il1', '432.jm1', '432.jr1', '648.bd1', '648.cy1', '648.dc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41050807, 39366316080, 1521641955, 39957120, 1481684400, 1134000], 'label': '46656.ir.216.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '216.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cl1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712243
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bl1', '72.bn1', '108.bd1'], 'contains': ['432.bk1', '432.bt1', '432.bw1', '432.im1', '432.in1', '432.jo1', '432.jt1', '648.be1', '648.cz1', '648.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 39916800, 6227827207, 104], 'label': '46656.ir.216.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cm1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712244
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bm1', '108.bp1', '108.bs1', '108.co1'], 'contains': ['432.bm1', '432.bp1', '432.is1', '432.kd1', '432.kj1', '648.bf1', '648.dc1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 1481684400, 269279866800, 1134000], 'label': '46656.ir.216.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712245
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bn1', '108.x1', '108.bs1', '108.cq1'], 'contains': ['432.bm1', '432.bv1', '432.it1', '432.kf1', '432.km1', '648.bg1', '648.dd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.216.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.co1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712246
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1', '108.z1', '108.bs1', '108.cp1'], 'contains': ['432.bm1', '432.kt1', '432.ku1', '648.bh1', '1944.cc1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 39916800, 269279866800], 'label': '46656.ir.216.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712247
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1', '108.z1', '108.bp1', '108.cq1'], 'contains': ['432.bm1', '432.kv1', '432.kw1', '648.bi1', '1944.cd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 39916800, 269279866800], 'label': '46656.ir.216.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cq1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712248
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '108.bm1'], 'contains': ['432.cd1', '432.mg1', '432.mh1', '648.bj1', '1944.ce1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 6267669018, 268280812800, 325, 39916800, 355419187304], 'label': '46656.ir.216.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.o1', 'old_label': '216.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cr1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712249
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.q1'], 'contains': ['432.cf2', '432.mi1', '432.mj1', '648.bl1', '1944.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 6267669018, 268280812800, 357818272567, 39916800, 357817869685], 'label': '46656.ir.216.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '216.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cs1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712250
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '8.h1', '8.m1', '8.n1'], 'contains': ['32.a1', '32.d1', '32.g1', '48.n1', '48.s1', '48.t1', '48.u1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6267744007, 39366316080, 455255499150, 7, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.16.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216712251
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '108.bc1'], 'contains': ['432.ch1', '432.mk1', '432.ml1', '648.bk1', '1944.ce1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 6267669018, 1481684400, 1174789, 39916800, 269279866800], 'label': '46656.ir.216.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '216.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ct1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712252
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bq1', '72.bs1', '108.cl1'], 'contains': ['432.b1', '432.m1', '432.bb1', '432.bn1', '432.cj1', '432.ds1', '432.jm1', '648.bm1', '648.de1', '648.df1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 39916800, 1521641624], 'label': '46656.ir.216.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '216.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712253
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bq1', '72.bt1', '108.bt1', '108.bu1', '108.bv1'], 'contains': ['432.c1', '432.o1', '432.bc1', '432.bs1', '432.ck1', '432.ek1', '432.jn1', '648.bn1', '648.df1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 7, 325, 39916800, 31697930984, 37885034880], 'label': '46656.ir.216.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '216.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712254
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.br1', '72.bz1'], 'contains': ['432.l1', '432.t1', '432.bq1', '432.cb1', '432.ci1', '432.jh1', '432.jq1', '648.bu1', '648.dg1', '648.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41050807, 39957120, 39366316405, 39916800, 31697930984, 37885034880], 'label': '46656.ir.216.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '216.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cw1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712255
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.br1', '72.ca1', '108.cl1'], 'contains': ['432.m1', '432.u1', '432.br1', '432.cc1', '432.cj1', '432.ji1', '432.jr1', '648.bt1', '648.dg1', '648.dh1', '648.di1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41050807, 39366316080, 1521641955, 39957120, 1481684400, 39916800], 'label': '46656.ir.216.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '216.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cx1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712256
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1', '72.cb1', '108.bv1'], 'contains': ['432.n1', '432.w1', '432.bs1', '432.cd1', '432.ck1', '432.jk1', '432.js1', '648.bv1', '648.dg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41050807, 39957120, 325, 39916800, 31697930984, 37885034880], 'label': '46656.ir.216.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cy1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712257
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ch1', '108.bv1', '108.bw1', '108.bx1'], 'contains': ['432.i1', '432.y1', '432.bj1', '432.ck1', '432.jx1', '648.cx1', '648.dj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39916800, 31697930984, 37885034880], 'label': '46656.ir.216.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cz1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712258
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bs1', '108.by1', '108.bz1', '108.ca1', '108.cb1', '108.cc1', '108.cd1', '108.co1'], 'contains': ['432.z1', '432.bp1', '432.cn1', '432.cs1', '432.kd1', '648.de1', '648.dk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 39916800, 269279866800], 'label': '46656.ir.216.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.da1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712259
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bs1', '72.bt1', '108.ce1', '108.cf1', '108.cl1'], 'contains': ['432.bb1', '432.br1', '432.cl1', '432.dt1', '432.ke1', '648.df1', '648.dk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 31697931315, 39916800, 37885034880], 'label': '46656.ir.216.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '216.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.db1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712260
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bu1', '72.bv1', '72.bw1', '108.ce1', '108.cg1', '108.cm1'], 'contains': ['432.cl1', '432.hu1', '432.kn1', '648.dl1', '1944.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 6227827200, 40320], 'label': '46656.ir.216.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '216.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dc1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712261
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '8.i1', '8.k1', '8.m1'], 'contains': ['32.a1', '48.b1', '48.z1', '48.bd1', '144.bl1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 499, 7, 325, 269279866800, 461482882830], 'label': '46656.ir.16.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216712262
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bu1', '72.bv1', '108.ch1'], 'contains': ['432.cm1', '432.hv1', '432.kr1', '648.dl1', '1944.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 270715783064, 1174320, 1481684400, 6227827200, 40320], 'label': '46656.ir.216.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '216.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dd1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712263
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.er1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bv1', '108.by1', '108.ci1', '108.cp1'], 'contains': ['432.cn1', '432.hw1', '432.kt1', '648.dl1', '1944.bd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 269279866800, 6227827200, 40320], 'label': '46656.ir.216.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.de1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712264
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bx1', '72.by1', '108.cf1', '108.cj1', '108.cm1'], 'contains': ['432.cl1', '432.jy1', '432.ko1', '648.dm1', '1944.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267381120, 39366316080, 1481684835, 1174320, 1481684400, 40320], 'label': '46656.ir.216.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '216.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.df1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712265
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1', '108.bz1', '108.ck1', '108.cp1'], 'contains': ['432.cn1', '432.jz1', '432.ku1', '648.dm1', '1944.bg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 269279866800, 40320], 'label': '46656.ir.216.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712266
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bz1', '72.ca1', '72.cb1', '108.cg1', '108.cj1', '108.cl1'], 'contains': ['432.bn1', '432.cc1', '432.cl1', '432.ka1', '432.kh1', '648.dg1', '648.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 39916800, 31697930984, 37885034880], 'label': '46656.ir.216.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712267
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bz1', '72.ca1', '108.ch1'], 'contains': ['432.bo1', '432.cg1', '432.cm1', '432.kb1', '432.ki1', '648.dh1', '648.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 39916800, 37885034880, 1521641624], 'label': '46656.ir.216.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '216.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.di1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712268
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ca1', '108.ci1', '108.ck1', '108.co1'], 'contains': ['432.bp1', '432.ch1', '432.cn1', '432.kc1', '432.kj1', '648.di1', '648.dn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 1481684400, 39916800, 269279866800], 'label': '46656.ir.216.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dj1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712269
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1', '108.by1', '108.ck1', '108.cq1'], 'contains': ['432.cn1', '432.kf1', '432.kv1', '648.do1', '1944.bk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 269279866800, 40320, 6227827207], 'label': '46656.ir.216.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dk1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712270
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cc1', '72.cd1', '108.ce1', '108.cj1', '108.cn1'], 'contains': ['432.cl1', '432.kg1', '432.kp1', '648.do1', '1944.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 40320, 6227827207], 'label': '46656.ir.216.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '216.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dl1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712271
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ce1', '72.cf1', '72.cg1', '108.cf1', '108.cg1', '108.cn1'], 'contains': ['432.cl1', '432.kk1', '432.kq1', '648.dp1', '1944.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 6267381127, 1481684835, 1174320, 1481684400, 40320], 'label': '46656.ir.216.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dm1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712272
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '8.i1', '8.l1', '8.n1'], 'contains': ['32.a1', '48.w1', '48.ba1', '144.bm1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 7, 6227827818, 325, 269279866800, 461482882830], 'label': '46656.ir.16.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216712273
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ce1', '72.cf1', '108.ch1'], 'contains': ['432.cm1', '432.kl1', '432.ks1', '648.dp1', '1944.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 40320, 270715783395], 'label': '46656.ir.216.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '216.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712274
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cf1', '108.bz1', '108.ci1', '108.cq1'], 'contains': ['432.cn1', '432.km1', '432.kw1', '648.dp1', '1944.bn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 269279866800, 40320], 'label': '46656.ir.216.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.do1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712275
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ch1', '72.ci1', '108.cl1', '108.cm1', '108.cn1'], 'contains': ['432.k1', '432.bl1', '432.cj1', '432.cl1', '432.kx1', '648.dj1', '648.dq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 39916800, 31697930984, 37885034880], 'label': '46656.ir.216.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '216.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dp1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712276
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1', '72.cs1', '108.x1', '108.cr1', '108.cs1'], 'contains': ['432.co1', '432.cr1', '432.ct1', '432.gp1', '432.ho1', '432.it1', '432.lz1', '648.dr1', '648.dx1', '648.dy1', '648.dz1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.216.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dq1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712277
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '72.cl1', '108.v1', '108.cr1', '108.ct1'], 'contains': ['432.co1', '432.cw1', '432.cy1', '648.ds1', '648.ea1', '648.ee1', '648.ei1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 499, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.216.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712278
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1', '108.v1', '108.cs1', '108.cu1'], 'contains': ['432.co1', '432.cx1', '432.db1', '648.dt1', '648.eb1', '648.ef1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40819, 39366316080, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.216.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ds1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712336
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1', '72.dm1', '108.c1', '108.dv1', '108.ef1'], 'contains': ['432.ec1', '432.fd1', '432.ff1', '648.ha1', '1944.cr1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.216.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fs1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712279
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '108.w1', '108.cs1', '108.ct1'], 'contains': ['432.co1', '432.cy1', '432.da1', '648.du1', '648.ec1', '648.eg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 41051299, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.216.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712280
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '72.cm1', '108.w1', '108.cr1', '108.cu1'], 'contains': ['432.co1', '432.cz1', '432.db1', '648.dv1', '648.ed1', '648.eh1', '648.ej1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091619, 39366316080, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.216.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.du1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712281
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ct1', '108.x1', '108.by1', '108.ct1', '108.cu1', '108.cv1', '108.cw1', '108.cx1'], 'contains': ['432.co1', '432.cs1', '432.gy1', '432.hw1', '432.kf1', '648.em1', '648.en1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.216.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dv1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712282
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ck1', '72.cu1', '108.cy1'], 'contains': ['432.cp1', '432.cq1', '432.cu1', '432.hx1', '432.hy1', '432.iq1', '432.mb1', '648.dw1', '648.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 624302466480, 7, 270715782960, 40323593520, 6227827207], 'label': '46656.ir.216.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '216.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dw1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712283
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '8.j1', '8.k1', '8.n1'], 'contains': ['32.a1', '48.c1', '48.bb1', '144.bn1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 7, 41091619, 325, 269279866800, 461482882830], 'label': '46656.ir.16.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216712284
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '72.cl1', '108.cy1'], 'contains': ['432.cp1', '432.dc1', '432.dd1', '648.ei1', '648.ek1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 499, 655477406640, 444, 269279866800, 6227389164], 'label': '46656.ir.216.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '216.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dx1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712285
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1', '72.cm1', '108.cy1'], 'contains': ['432.cp1', '432.de1', '432.df1', '648.ej1', '648.el1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091619, 39366316080, 655477406640, 444, 269279866800, 6227389164], 'label': '46656.ir.216.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '216.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dy1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712286
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '72.cn1', '108.cy1'], 'contains': ['432.cq1', '432.dc1', '432.de1', '648.eo1', '648.ey1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 655477406640, 444, 269279866800], 'label': '46656.ir.216.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '216.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dz1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712287
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '72.co1', '108.cy1'], 'contains': ['432.cq1', '432.dd1', '432.df1', '648.ep1', '648.ez1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 469, 624302466480, 270715782960, 6227827818, 40323593520], 'label': '46656.ir.216.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '216.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ea1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712288
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '72.cn1', '108.y1', '108.cr1'], 'contains': ['432.cr1', '432.cw1', '432.cz1', '648.eq1', '648.eu1', '648.ey1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 1481684400, 269279866800, 1481684844], 'label': '46656.ir.216.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eb1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712289
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1', '108.y1', '108.ba1', '108.cs1'], 'contains': ['432.cr1', '432.cx1', '432.da1', '648.er1', '648.ev1', '648.ew1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 269279866800, 39957619, 1481684844], 'label': '46656.ir.216.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ec1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712290
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '72.co1', '108.bb1', '108.cr1', '108.cs1'], 'contains': ['432.cr1', '432.cy1', '432.db1', '648.es1', '648.et1', '648.ex1', '648.ez1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 469, 39366316080, 1481684400, 6227827818, 269279866800], 'label': '46656.ir.216.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ed1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712291
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cv1', '108.x1', '108.bz1', '108.cz1', '108.da1', '108.db1', '108.dc1', '108.dl1'], 'contains': ['432.cs1', '432.ct1', '432.jz1', '432.km1', '432.mf1', '648.fa1', '648.fj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400, 269279866800], 'label': '46656.ir.216.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ee1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712292
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1', '108.y1', '108.ca1', '108.ct1', '108.cz1', '108.dd1', '108.de1', '108.dm1'], 'contains': ['432.cs1', '432.cw1', '432.da1', '648.fb1', '648.ff1', '648.fk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 499, 1481684400, 1521641964, 269279866800], 'label': '46656.ir.216.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ef1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712293
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cw1', '108.z1', '108.by1', '108.dd1', '108.df1', '108.dg1', '108.dh1', '108.dl1'], 'contains': ['432.cs1', '432.kt1', '432.kv1', '648.fl1', '1944.dt1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 6227464327, 269279866800], 'label': '46656.ir.216.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eg1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712294
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1', '8.j1', '8.l1', '8.m1'], 'contains': ['32.a1', '48.y1', '48.bc1', '48.be1', '144.bo1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6267744618, 455255499150, 7, 325, 269279866800], 'label': '46656.ir.16.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216712295
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1', '108.y1', '108.cb1', '108.cu1', '108.da1', '108.df1', '108.di1', '108.dn1'], 'contains': ['432.cs1', '432.cx1', '432.cz1', '648.fc1', '648.fg1', '648.fm1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 1521641964, 269279866800, 1134499], 'label': '46656.ir.216.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712296
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1', '108.ba1', '108.ca1', '108.cv1', '108.db1', '108.dg1', '108.dj1', '108.dn1'], 'contains': ['432.cs1', '432.cx1', '648.fh1', '648.fn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39366316080, 39957120, 1481684400, 1521641964, 269279866800], 'label': '46656.ir.216.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ei1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712297
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1', '108.z1', '108.bz1', '108.cx1', '108.de1', '108.di1', '108.dj1', '108.dk1'], 'contains': ['432.cs1', '432.ku1', '432.kw1', '648.fo1', '1944.dw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400, 269279866800], 'label': '46656.ir.216.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ej1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712298
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1', '108.bb1', '108.cc1', '108.ct1', '108.da1', '108.dg1', '108.dk1', '108.do1'], 'contains': ['432.cs1', '432.cy1', '648.fd1', '648.fp1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 6227827818, 269279866800], 'label': '46656.ir.216.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ek1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712299
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1', '108.ba1', '108.cb1', '108.cw1', '108.dc1', '108.dh1', '108.dk1', '108.dm1'], 'contains': ['432.cs1', '432.da1', '648.fi1', '648.fq1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 41051299, 1481684400, 1521641964, 269279866800], 'label': '46656.ir.216.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.el1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712300
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '108.bb1', '108.cd1', '108.cu1', '108.cz1', '108.dh1', '108.dj1', '108.dp1'], 'contains': ['432.cs1', '432.db1', '648.fe1', '648.fr1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 6267744618, 269279866800], 'label': '46656.ir.216.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.em1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712301
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '108.bc1', '108.cc1', '108.cv1', '108.dc1', '108.dd1', '108.di1', '108.dp1'], 'contains': ['432.cs1', '432.mk1', '648.fs1', '1944.ea1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 39366316080, 6227464938, 1174320, 1481684400, 269279866800], 'label': '46656.ir.216.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.en1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712302
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '108.bc1', '108.cd1', '108.cw1', '108.db1', '108.de1', '108.df1', '108.do1'], 'contains': ['432.cs1', '432.ml1', '648.ft1', '1944.eb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 6267381738, 269279866800], 'label': '46656.ir.216.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eo1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712303
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cp1', '72.cy1', '108.co1', '108.cx1', '108.dl1', '108.dm1', '108.dn1', '108.do1', '108.dp1'], 'contains': ['432.a1', '432.cs1', '432.kj1', '648.fu1'], 'core': '432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 7, 1481684400, 269279866800], 'label': '46656.ir.216.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ep1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712304
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '72.cq1', '108.v1', '108.cr1', '108.cz1'], 'contains': ['432.ct1', '432.cw1', '432.db1', '648.fv1', '648.fz1', '648.gd1', '648.gf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684537, 7, 1481684400, 269279866800], 'label': '46656.ir.216.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712305
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '8.h1'], 'contains': ['32.b1', '32.c1', '32.d1', '48.bf1', '48.bk1', '48.bl1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827200, 461482882830], 'label': '46656.ir.16.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '1296.838'}
  • id: 216712306
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1', '108.v1', '108.cs1', '108.da1'], 'contains': ['432.ct1', '432.cx1', '432.cy1', '648.fw1', '648.ga1', '648.gg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43633820302, 6267744007, 39366316080, 7, 1481684400, 269279866800], 'label': '46656.ir.216.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.er1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712307
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1', '72.cr1', '108.w1', '108.cr1', '108.da1'], 'contains': ['432.ct1', '432.cy1', '432.cz1', '648.fx1', '648.gb1', '648.ge1', '648.gh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1481684400, 269279866800, 24952072462], 'label': '46656.ir.216.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.es1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712308
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1', '108.w1', '108.cs1', '108.cz1'], 'contains': ['432.ct1', '432.da1', '432.db1', '648.fy1', '648.gc1', '648.gi1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 2918003897, 39366316080, 7, 1481684400, 269279866800], 'label': '46656.ir.216.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.et1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712309
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1', '72.cq1', '108.cy1'], 'contains': ['432.cu1', '432.dc1', '432.df1', '648.gd1', '648.gj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 137, 7, 655477406640, 269279866800], 'label': '46656.ir.216.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '216.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.eu1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712310
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ce1', '72.cr1', '108.cy1'], 'contains': ['432.cu1', '432.dd1', '432.de1', '648.ge1', '648.gk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6227388862, 6267744007, 39366316080, 7, 655477406640, 269279866800], 'label': '46656.ir.216.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '216.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ev1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712311
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1', '72.cq1'], 'contains': ['432.cv1', '432.dg1', '432.dh1', '648.gd1', '648.gl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 137, 7, 269279866800, 623823424560], 'label': '46656.ir.216.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '216.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ew1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216712312
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cs1', '72.cz1', '108.bd1'], 'contains': ['432.di1', '432.do1', '432.dx1', '432.fs1', '432.gb1', '432.im1', '432.lx1', '648.dr1', '648.gm1', '648.gn1', '648.go1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 7, 6227827207, 104], 'label': '46656.ir.216.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ex1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712313
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cu1', '72.de1'], 'contains': ['432.dm1', '432.dn1', '432.dy1', '432.gl1', '432.hc1', '432.id1', '432.ma1', '648.dw1', '648.gn1', '648.gq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 387999647280, 7, 325, 6227827207, 568299191498], 'label': '46656.ir.216.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '216.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ey1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712314
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cs1', '72.df1', '108.bd1'], 'contains': ['432.dj1', '432.do1', '432.du1', '432.gm1', '432.hf1', '432.in1', '432.lf1', '648.dx1', '648.gm1', '648.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40323593624, 41091120, 268280812800, 7, 40323593520, 6227827207], 'label': '46656.ir.216.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ez1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712315
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cs1', '72.dg1', '108.a1'], 'contains': ['432.dk1', '432.dp1', '432.dv1', '432.gn1', '432.hg1', '432.io1', '432.lh1', '648.dy1', '648.go1', '648.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.216.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '216.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fa1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712316
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1', '8.h1'], 'contains': ['32.b1', '32.f1', '32.g1', '48.bi1', '48.bm1', '48.bn1', '48.bo1'], 'core': '96.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827200, 461482882830, 41091127], 'label': '46656.ir.16.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216712317
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cs1', '72.cu1', '72.dh1'], 'contains': ['432.dl1', '432.dq1', '432.dw1', '432.go1', '432.hh1', '432.ip1', '432.li1', '648.dz1', '648.gn1', '648.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.216.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '216.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712318
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ct1', '72.du1', '108.bd1'], 'contains': ['432.di1', '432.dj1', '432.dr1', '432.fx1', '432.gw1', '432.hr1', '432.jo1', '648.em1', '648.gp1', '648.gs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 1174320, 6227827207, 104], 'label': '46656.ir.216.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712319
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ct1', '72.dv1', '108.a1', '108.ce1', '108.dq1'], 'contains': ['432.dk1', '432.dt1', '432.gz1', '432.hu1', '432.kg1', '648.en1', '648.gs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.216.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '216.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fd1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712320
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cv1', '72.ei1', '108.bd1'], 'contains': ['432.dr1', '432.du1', '432.dx1', '432.jf1', '432.jt1', '432.lp1', '432.md1', '648.fa1', '648.gt1', '648.gw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 1174320, 104], 'label': '46656.ir.216.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fe1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712321
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cv1', '72.er1', '108.a1', '108.cf1', '108.dr1'], 'contains': ['432.dt1', '432.dv1', '432.jy1', '432.kk1', '432.ls1', '648.fj1', '648.gw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400, 1481684504], 'label': '46656.ir.216.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ff1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712322
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cw1', '72.et1', '108.b1', '108.ce1', '108.dr1'], 'contains': ['432.dt1', '432.kn1', '432.kp1', '648.fl1', '1944.fg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 7, 6227464327], 'label': '46656.ir.216.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '216.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712323
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cx1', '72.ew1', '108.b1', '108.cf1', '108.dq1'], 'contains': ['432.dt1', '432.ko1', '432.kq1', '648.fo1', '1944.fh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 7], 'label': '46656.ir.216.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712324
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cy1', '72.fc1', '108.cl1', '108.dq1', '108.dr1'], 'contains': ['432.ds1', '432.dt1', '432.jr1', '432.kh1', '432.kx1', '648.fu1', '648.gy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 7, 31697931315, 37885034880], 'label': '46656.ir.216.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fi1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712325
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cz1', '72.df1', '108.bg1', '108.ds1', '108.dt1'], 'contains': ['432.ea1', '432.eg1', '432.en1', '432.fp1', '432.gf1', '432.if1', '432.ll1', '648.gm1', '648.gz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.216.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fj1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712326
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cz1', '72.de1', '72.dh1', '108.du1'], 'contains': ['432.eb1', '432.eh1', '432.eo1', '432.fq1', '432.gg1', '432.ig1', '432.lm1', '648.gn1', '648.gz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 387999647280, 7, 325, 6227827207, 387999647384], 'label': '46656.ir.216.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '216.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fk1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712327
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['11664.bn1', '11664.q1', '11664.bm1', '11664.n1', '11664.l1', '11664.o1', '11664.m1', '11664.p1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.f1', '8.g1', '12.y1', '12.z1', '12.ba1', '16.k1', '108.bq1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '46656.ir', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712328
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '8.h1'], 'contains': ['32.c1', '32.e1', '32.g1', '48.bp1', '48.br1', '48.bs1', '48.bt1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207, 461482882830], 'label': '46656.ir.16.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216712329
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cz1', '72.dg1', '108.g1', '108.dv1', '108.dw1'], 'contains': ['432.ec1', '432.ei1', '432.ep1', '432.fr1', '432.gh1', '432.ih1', '432.ln1', '648.go1', '648.gz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 6227827207, 104], 'label': '46656.ir.216.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fl1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712330
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1', '72.di1', '108.be1', '108.ds1', '108.dx1'], 'contains': ['432.ea1', '432.er1', '432.eu1', '648.ha1', '1944.cl1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 499, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.216.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fm1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712331
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.db1', '72.dj1', '108.be1', '108.dt1', '108.dz1'], 'contains': ['432.ea1', '432.et1', '432.ey1', '648.hb1', '1944.cm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39917299, 268280812800, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.216.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fn1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712332
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dc1', '72.dk1', '108.bf1', '108.dt1', '108.dx1'], 'contains': ['432.ea1', '432.eu1', '432.ew1', '648.hc1', '1944.cn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 1174819, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.216.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fo1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712333
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1', '72.dl1', '108.bf1', '108.ds1', '108.dz1'], 'contains': ['432.ea1', '432.ev1', '432.ey1', '648.hd1', '1944.co1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091619, 268280812800, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.216.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fp1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712334
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1', '72.dq1', '72.ds1', '108.du1'], 'contains': ['432.eb1', '432.ez1', '432.fa1', '648.ha1', '1944.cp1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6227827207, 387999647384, 499, 7, 325, 387999647280], 'label': '46656.ir.216.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cf1', 'old_label': '216.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fq1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712335
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1', '72.dr1', '72.dt1', '108.du1'], 'contains': ['432.eb1', '432.fb1', '432.fc1', '648.hd1', '1944.cq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091619, 387999647280, 7, 325, 6227827207, 387999647384], 'label': '46656.ir.216.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '216.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fr1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712337
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.db1', '72.dn1', '108.c1', '108.dw1', '108.eg1'], 'contains': ['432.ec1', '432.fe1', '432.fj1', '648.hb1', '1944.cs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39917299, 39366316080, 7, 325, 6227827207, 104], 'label': '46656.ir.216.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ft1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712338
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dc1', '72.do1', '108.d1', '108.dw1', '108.ef1'], 'contains': ['432.ec1', '432.fg1', '432.fi1', '648.hc1', '1944.ct1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174819, 6227827207, 7, 104, 325], 'label': '46656.ir.216.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712339
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1', '8.h1'], 'contains': ['32.d1', '32.e1', '32.f1', '48.ch1', '48.ci1', '48.ck1'], 'core': '96.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207, 461482882830, 41091127], 'label': '46656.ir.16.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '16.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216712340
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1', '72.dp1', '108.d1', '108.dv1', '108.eg1'], 'contains': ['432.ec1', '432.fh1', '432.fk1', '648.hd1', '1944.cu1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 6227827207, 7, 104, 41091619, 325], 'label': '46656.ir.216.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712341
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.du1', '108.n1', '108.bg1', '108.dx1', '108.dy1', '108.dz1', '108.ea1', '108.eb1'], 'contains': ['432.ea1', '432.ej1', '432.fz1', '432.gi1', '432.ix1', '648.gp1', '648.he1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 355419187304, 6227827207, 1174645], 'label': '46656.ir.216.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fw1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712342
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.l1', '72.de1', '108.ec1'], 'contains': ['432.ee1', '432.ef1', '432.eq1', '432.gj1', '432.he1', '432.hz1', '432.lo1', '648.gq1', '648.gz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 7, 325, 174452060430, 6227827207, 104], 'label': '46656.ir.216.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '216.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fx1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712343
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.df1', '72.dg1', '72.dh1', '108.g1', '108.ed1', '108.ee1'], 'contains': ['432.ed1', '432.ei1', '432.em1', '432.gk1', '432.hl1', '432.ii1', '432.kz1', '648.gr1', '648.gz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.216.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fy1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712344
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.di1', '72.dm1', '72.dq1', '108.e1', '108.ed1', '108.ef1'], 'contains': ['432.ed1', '432.fd1', '432.fg1', '648.ha1', '1944.cy1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 499, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.216.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '216.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.fz1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712345
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dj1', '72.dn1', '108.e1', '108.ee1', '108.eg1'], 'contains': ['432.ed1', '432.fe1', '432.fk1', '648.hb1', '1944.cz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 39917299, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.216.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ga1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712346
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dk1', '72.do1', '108.f1', '108.ee1', '108.ef1'], 'contains': ['432.ed1', '432.ff1', '432.fi1', '648.hc1', '1944.da1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 1174819, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.216.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gb1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712347
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dl1', '72.dp1', '72.dr1', '108.f1', '108.ed1', '108.eg1'], 'contains': ['432.ed1', '432.fh1', '432.fj1', '648.hd1', '1944.db1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091619, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.216.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gc1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712348
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bh1', '72.ds1', '108.ec1'], 'contains': ['432.ee1', '432.fl1', '432.fm1', '648.ha1', '1944.dc1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6227827207, 499, 7, 104, 325, 461482882830], 'label': '46656.ir.216.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '216.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gd1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712349
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bi1', '72.dt1', '108.ec1'], 'contains': ['432.ee1', '432.fn1', '432.fo1', '648.hd1', '1944.dd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091619, 7, 325, 174452060430, 6227827207, 104], 'label': '46656.ir.216.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '216.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ge1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712350
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.b1', '36.c1', '36.d1', '36.e1', '36.h1', '36.ck1', '36.cl1', '36.cp1', '36.cq1', '36.cw1', '36.cx1', '54.a1', '162.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 1174645, 1174320, 6227827207, 499, 7], 'label': '46656.ir.18.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712351
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.du1', '72.dv1', '108.g1', '108.ef1', '108.eg1'], 'contains': ['432.ec1', '432.ed1', '432.el1', '432.ga1', '432.hb1', '432.ht1', '432.jp1', '648.gs1', '648.he1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 6227827207, 7, 104], 'label': '46656.ir.216.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gf1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712352
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.m1', '72.dw1', '108.ec1'], 'contains': ['432.ef1', '432.fl1', '432.fn1', '648.hf1', '1944.df1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 499, 7, 325, 174452060430, 104], 'label': '46656.ir.216.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '216.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gg1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712353
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.n1', '72.dx1', '108.ec1'], 'contains': ['432.ef1', '432.fm1', '432.fo1', '648.hh1', '1944.dg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 7, 325, 174452060430, 6227827818, 104], 'label': '46656.ir.216.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '216.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gh1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712354
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dy1', '72.ec1', '108.h1', '108.bi1', '108.ds1'], 'contains': ['432.eg1', '432.er1', '432.ev1', '648.hf1', '1944.dh1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 499, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.216.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gi1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712355
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ed1', '72.ee1', '108.h1', '108.i1', '108.bk1'], 'contains': ['432.eg1', '432.es1', '432.ex1', '648.hg1', '1944.di1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 7, 325, 31658054504, 39957619, 37885034880], 'label': '46656.ir.216.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gj1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712356
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dz1', '72.ee1', '108.i1', '108.bi1', '108.dt1'], 'contains': ['432.eg1', '432.et1', '432.ew1', '648.hg1', '1944.dj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 7, 325, 1481684400, 1481684504, 39957619], 'label': '46656.ir.216.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gk1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712357
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ea1', '72.eb1', '108.bl1', '108.ds1', '108.dt1'], 'contains': ['432.eg1', '432.eu1', '432.ey1', '648.hh1', '1944.dk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 325, 6227827818, 355419187304], 'label': '46656.ir.216.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gl1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712358
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dw1', '72.dy1', '72.eg1', '108.du1'], 'contains': ['432.eh1', '432.ez1', '432.fb1', '648.hf1', '1944.dl1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 301891126320, 499, 7, 325, 104], 'label': '46656.ir.216.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '216.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gm1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712359
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dx1', '72.ea1', '72.eh1', '108.du1'], 'contains': ['432.eh1', '432.fa1', '432.fc1', '648.hh1', '1944.dm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 387999647280, 7, 325, 6227827818, 387999647384], 'label': '46656.ir.216.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '216.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gn1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712360
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dy1', '72.ec1', '72.eg1', '108.j1', '108.dv1', '108.ed1'], 'contains': ['432.ei1', '432.fd1', '432.fh1', '648.hf1', '1944.dn1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 7, 325, 104], 'label': '46656.ir.216.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.go1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712361
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.d1', '36.g1', '36.i1', '36.cr1', '36.cs1', '36.cy1', '36.cz1', '162.b1', '162.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 1174645, 1174320, 6227827207, 7, 39957619], 'label': '46656.ir.18.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712362
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dz1', '72.ed1', '108.j1', '108.dw1', '108.ee1'], 'contains': ['432.ei1', '432.fe1', '432.fi1', '648.hg1', '1944.do1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 387037284480, 7, 325, 39957619, 104], 'label': '46656.ir.216.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gp1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712363
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ea1', '72.ef1', '108.k1', '108.dv1', '108.ee1'], 'contains': ['432.ei1', '432.ff1', '432.fk1', '648.hh1', '1944.dp1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 6227827818, 104], 'label': '46656.ir.216.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gq1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712364
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eb1', '72.ef1', '72.eh1', '108.k1', '108.dw1', '108.ed1'], 'contains': ['432.ei1', '432.fg1', '432.fj1', '648.hh1', '1944.dq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 325, 6227827818, 40323593520], 'label': '46656.ir.216.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gr1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712365
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ei1', '108.o1', '108.bg1', '108.ei1', '108.ej1', '108.ek1', '108.el1', '108.fb1'], 'contains': ['432.ej1', '432.en1', '432.iu1', '432.iz1', '432.lr1', '648.gt1', '648.hi1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gs1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712366
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ej1', '72.en1', '108.p1', '108.bi1', '108.dx1', '108.ei1', '108.em1', '108.en1', '108.fc1'], 'contains': ['432.ej1', '432.er1', '432.ew1', '648.hj1', '1944.ds1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1481684400, 39957120, 499, 7, 325, 1521641624], 'label': '46656.ir.216.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gt1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712367
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1', '108.n1', '108.bj1', '108.em1', '108.eo1', '108.ep1', '108.eq1', '108.fb1'], 'contains': ['432.ej1', '432.ja1', '432.jc1', '648.gu1', '648.hk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 355419187304, 1174645], 'label': '46656.ir.216.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gu1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712368
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ep1', '108.p1', '108.bk1', '108.dy1', '108.ej1', '108.eo1', '108.er1', '108.fd1'], 'contains': ['432.ej1', '432.es1', '648.hm1', '1944.du1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39957120, 7, 325, 1481684400, 1521641624], 'label': '46656.ir.216.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gv1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712369
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ek1', '72.eo1', '108.q1', '108.bi1', '108.dz1', '108.ek1', '108.ep1', '108.es1', '108.fd1'], 'contains': ['432.ej1', '432.et1', '432.ev1', '648.hl1', '1944.dv1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 7, 325, 1481684400, 1134499, 1521641624], 'label': '46656.ir.216.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712370
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1', '108.o1', '108.bj1', '108.eb1', '108.en1', '108.er1', '108.es1', '108.et1'], 'contains': ['432.ej1', '432.jb1', '432.jd1', '648.gv1', '648.hn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381127, 268280812800, 7, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gx1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712371
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.el1', '108.r1', '108.bl1', '108.dx1', '108.ek1', '108.eo1', '108.et1', '108.fe1'], 'contains': ['432.ej1', '432.eu1', '648.ho1', '1944.dx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227827818, 355419187304, 1174645], 'label': '46656.ir.216.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gy1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712372
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '9.a1'], 'contains': ['36.e1', '36.f1', '36.i1', '36.da1', '36.db1', '36.dc1', '36.df1', '162.c1', '162.g1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6267381127, 499, 7], 'label': '46656.ir.18.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712373
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eq1', '108.q1', '108.bk1', '108.ea1', '108.el1', '108.eq1', '108.et1', '108.fc1'], 'contains': ['432.ej1', '432.ex1', '648.hp1', '1944.dy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1481684400, 39957120, 7, 41051299, 325, 1521641624], 'label': '46656.ir.216.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.gz1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712374
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.em1', '108.s1', '108.bl1', '108.dz1', '108.ei1', '108.eq1', '108.er1', '108.ff1'], 'contains': ['432.ej1', '432.ey1', '648.hq1', '1944.dz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 6267744618, 7, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ha1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712375
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '108.r1', '108.bm1', '108.dy1', '108.el1', '108.em1', '108.es1', '108.ff1'], 'contains': ['432.ej1', '432.mg1', '648.hr1', '1944.ea1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 6227464938, 7, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hb1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712376
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '108.s1', '108.bm1', '108.ea1', '108.ej1', '108.en1', '108.ep1', '108.fe1'], 'contains': ['432.ej1', '432.mh1', '648.hs1', '1944.eb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6267381738, 355419187304, 1174645], 'label': '46656.ir.216.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hc1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712377
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ei1', '72.er1', '108.g1', '108.eu1', '108.ev1'], 'contains': ['432.el1', '432.em1', '432.ep1', '432.je1', '432.jv1', '432.la1', '432.lu1', '648.gw1', '648.hi1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 104, 1174645], 'label': '46656.ir.216.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hd1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712378
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.en1', '72.es1', '108.h1', '108.bt1', '108.fc1'], 'contains': ['432.ek1', '432.er1', '432.ex1', '648.hj1', '1944.ed1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 37885034880, 499, 7, 325, 31697930984], 'label': '46656.ir.216.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '216.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.he1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712379
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eo1', '72.eu1', '108.h1', '108.bu1', '108.fd1'], 'contains': ['432.ek1', '432.es1', '432.ev1', '648.hl1', '1944.ee1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 7, 325, 1134499, 31697930984, 37885034880], 'label': '46656.ir.216.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hf1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712380
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ep1', '72.ev1', '108.i1', '108.bt1', '108.fd1'], 'contains': ['432.ek1', '432.es1', '432.et1', '648.hm1', '1944.ef1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39917299, 39957120, 7, 325, 31697930984, 37885034880], 'label': '46656.ir.216.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '216.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hg1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712381
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eq1', '72.ey1', '108.i1', '108.bu1', '108.fc1'], 'contains': ['432.ek1', '432.ew1', '432.ex1', '648.hp1', '1944.eg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 37885034880, 7, 41051299, 325, 31697930984], 'label': '46656.ir.216.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '216.hh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hh1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712382
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ej1', '72.es1', '108.j1', '108.ef1', '108.eu1'], 'contains': ['432.el1', '432.fd1', '432.fi1', '648.hj1', '1944.eh1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [387037284480, 39957120, 499, 7, 325, 39957224], 'label': '46656.ir.216.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.hi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hi1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712383
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '9.a1'], 'contains': ['36.f1', '36.g1', '36.h1', '36.dd1', '36.de1', '36.dg1', '36.dh1', '162.d1', '162.h1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6267381127, 7, 39957619], 'label': '46656.ir.18.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712384
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ek1', '72.eu1', '108.j1', '108.eg1', '108.ev1'], 'contains': ['432.el1', '432.fe1', '432.fh1', '648.hl1', '1944.ei1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 39957120, 7, 325, 39957224, 1134499], 'label': '46656.ir.216.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.hj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hj1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712385
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.el1', '72.ex1', '108.k1', '108.ef1', '108.ev1'], 'contains': ['432.el1', '432.ff1', '432.fg1', '648.ho1', '1944.ej1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 6227827818, 104, 1174645], 'label': '46656.ir.216.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.hk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hk1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712386
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.em1', '72.ez1', '108.k1', '108.eg1', '108.eu1'], 'contains': ['432.el1', '432.fj1', '432.fk1', '648.hq1', '1944.ek1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 6267744618, 7, 104], 'label': '46656.ir.216.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.hl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hl1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712387
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '108.bh1', '108.eh1', '108.ew1', '108.ex1', '108.ey1', '108.ez1', '108.fa1'], 'contains': ['432.jw1', '648.gx1', '648.ht1', '864.ba1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 7, 41051125, 174452060430], 'label': '46656.ir.216.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.hm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hm1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216712388
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fc1', '108.bv1', '108.eb1', '108.fb1', '108.fc1', '108.fd1', '108.fe1', '108.ff1'], 'contains': ['432.ej1', '432.ek1', '432.iy1', '432.js1', '432.jx1', '648.gy1', '648.ht1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050800, 39957120, 37885034880, 7, 41051125, 31697930984], 'label': '46656.ir.216.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.hn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hn1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712389
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fd1', '72.fh1', '72.fl1', '108.c1', '108.ed1', '108.eu1'], 'contains': ['432.em1', '432.fd1', '432.fj1', '648.hu1', '1944.en1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 499, 7, 325, 104], 'label': '46656.ir.216.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.ho1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ho1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712390
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fe1', '72.fi1', '108.c1', '108.ee1', '108.ev1'], 'contains': ['432.em1', '432.fe1', '432.ff1', '648.hv1', '1944.eo1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 6227827818, 104], 'label': '46656.ir.216.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.hp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hp1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712391
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ff1', '72.fj1', '72.fm1', '108.d1', '108.ed1', '108.ev1'], 'contains': ['432.em1', '432.fg1', '432.fh1', '648.hw1', '1944.ep1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 6227389338, 104], 'label': '46656.ir.216.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.hq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hq1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712392
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fg1', '72.fk1', '108.d1', '108.ee1', '108.eu1'], 'contains': ['432.em1', '432.fi1', '432.fk1', '648.hx1', '1944.eq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174819, 7, 325, 104], 'label': '46656.ir.216.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.hr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hr1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712393
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fd1', '72.fn1', '108.be1', '108.ds1', '108.ei1'], 'contains': ['432.en1', '432.er1', '432.ey1', '648.hu1', '1944.er1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 268280812800, 499, 7, 325, 355419187304], 'label': '46656.ir.216.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.hs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hs1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712394
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['36.n1', '36.o1', '36.p1', '36.q1', '36.r1', '36.s1', '36.t1', '36.cf1', '36.cg1', '36.ci1', '36.cj1', '36.cn1', '36.co1', '36.cu1', '36.cv1', '54.a1', '54.j1', '162.m1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39916800, 1174645, 1174320, 268280812800, 6227827207, 499, 7, 104], 'label': '46656.ir.18.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '18.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712395
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fe1', '72.fo1', '108.be1', '108.dt1', '108.ek1'], 'contains': ['432.en1', '432.et1', '432.eu1', '648.hv1', '1944.es1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 325, 6227827818, 355419187304], 'label': '46656.ir.216.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '216.ht1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ht1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712396
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ff1', '72.fp1', '108.bf1', '108.ds1', '108.ek1'], 'contains': ['432.en1', '432.eu1', '432.ev1', '648.hw1', '1944.et1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 325, 6227389338, 355419187304], 'label': '46656.ir.216.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.hu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712397
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fg1', '72.fq1', '108.bf1', '108.dt1', '108.ei1'], 'contains': ['432.en1', '432.ew1', '432.ey1', '648.hx1', '1944.eu1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 268280812800, 1174819, 7, 325, 355419187304], 'label': '46656.ir.216.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.hv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712398
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fl1', '72.fn1', '72.fr1', '72.ft1', '108.du1'], 'contains': ['432.eo1', '432.ez1', '432.fc1', '648.hu1', '1944.ev1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 301891126320, 499, 7, 325, 104], 'label': '46656.ir.216.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '216.hw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712399
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fm1', '72.fp1', '72.fs1', '108.du1'], 'contains': ['432.eo1', '432.fa1', '432.fb1', '648.hw1', '1944.ew1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 301891126320, 7, 325, 6227389338, 104], 'label': '46656.ir.216.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '216.hx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hx1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712400
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fh1', '72.fn1', '108.e1', '108.dv1', '108.eu1'], 'contains': ['432.ep1', '432.fd1', '432.fk1', '648.hu1', '1944.ex1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744007, 499, 7, 325, 40323593520], 'label': '46656.ir.216.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.hy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hy1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712401
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fi1', '72.fo1', '108.e1', '108.dw1', '108.ev1'], 'contains': ['432.ep1', '432.fe1', '432.fg1', '648.hv1', '1944.ey1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744007, 7, 325, 6227827818, 40323593520], 'label': '46656.ir.216.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.hz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.hz1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712402
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fj1', '72.fp1', '108.f1', '108.dv1', '108.ev1'], 'contains': ['432.ep1', '432.ff1', '432.fh1', '648.hw1', '1944.ez1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 6267744007, 7, 325, 6227389338, 40323593520], 'label': '46656.ir.216.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.ia1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ia1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712403
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fk1', '72.fq1', '108.f1', '108.dw1', '108.eu1'], 'contains': ['432.ep1', '432.fi1', '432.fj1', '648.hx1', '1944.fa1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 6267744007, 1174819, 7, 325, 40323593520], 'label': '46656.ir.216.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.ib1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ib1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712404
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bj1', '72.fr1', '108.ec1'], 'contains': ['432.eq1', '432.fl1', '432.fo1', '648.hu1', '1944.fb1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 499, 7, 104, 325, 174451657230], 'label': '46656.ir.216.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '216.ic1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ic1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712405
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '9.a1'], 'contains': ['36.bc1', '36.be1', '36.bg1', '36.cp1', '36.cr1', '36.da1', '36.dd1', '162.i1', '162.s1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 499, 7, 40320], 'label': '46656.ir.18.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712406
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bk1', '72.fs1', '108.ec1'], 'contains': ['432.eq1', '432.fm1', '432.fn1', '648.hw1', '1944.fc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 7, 325, 174451657230, 6227389338, 104], 'label': '46656.ir.216.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '216.id1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.id1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712407
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fu1', '72.fv1', '108.g1'], 'contains': ['432.fr1', '432.fv1', '432.ga1', '432.ib1', '432.ii1', '432.ld1', '432.lu1', '648.hy1', '648.hz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091120, 1174327, 325, 40323593520, 6227827207], 'label': '46656.ir.216.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.ie1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ie1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712408
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fu1', '72.fw1', '108.bg1'], 'contains': ['432.fp1', '432.fw1', '432.fz1', '432.ic1', '432.if1', '432.le1', '432.lr1', '648.hy1', '648.ia1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 1174327, 268280812800, 325, 355419187304, 6227827207], 'label': '46656.ir.216.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '216.if1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.if1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712409
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fu1', '72.fx1', '108.bd1'], 'contains': ['432.fs1', '432.ft1', '432.fx1', '432.ik1', '432.in1', '432.lw1', '432.md1', '648.hz1', '648.ia1', '648.ib1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40323593624, 41091120, 1174327, 268280812800, 40323593520, 6227827207], 'label': '46656.ir.216.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.ig1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ig1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712410
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1', '108.n1', '108.bn1', '108.fg1'], 'contains': ['432.gi1', '432.iv1', '432.jc1', '648.ic1', '648.ig1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 268280812800, 1174320, 6227827200, 355419187304, 1174645], 'label': '46656.ir.216.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ih1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ih1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216712411
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fy1', '108.t1', '108.bg1', '108.fg1'], 'contains': ['432.fw1', '432.gf1', '432.gi1', '432.iw1', '432.iz1', '648.id1', '648.ie1', '648.if1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 268280812800, 1174320, 6227827200, 355419187304, 1174645], 'label': '46656.ir.216.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ii1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ii1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712412
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1', '108.t1', '108.bn1', '108.eb1'], 'contains': ['432.gi1', '432.iy1', '432.jd1', '648.ih1', '648.ii1', '648.ij1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 355419187304, 39957127, 1174645], 'label': '46656.ir.216.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ij1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ij1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712413
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1', '108.bw1', '108.eb1', '108.fg1'], 'contains': ['432.gi1', '432.jb1', '432.jx1', '648.ik1', '648.il1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 41051125, 6227827200], 'label': '46656.ir.216.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ik1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ik1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 216712414
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fv1', '72.fw1', '108.g1'], 'contains': ['432.gk1', '432.gv1', '432.hb1', '432.ib1', '432.ih1', '432.ky1', '432.la1', '648.hy1', '648.im1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 325, 6227827207, 104], 'label': '46656.ir.216.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.il1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.il1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712415
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fv1', '72.fx1', '108.a1'], 'contains': ['432.gn1', '432.gq1', '432.gz1', '432.ij1', '432.io1', '432.lb1', '432.ls1', '648.hz1', '648.im1', '648.in1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.216.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '216.im1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.im1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712416
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '9.a1'], 'contains': ['36.bc1', '36.bf1', '36.bh1', '36.cq1', '36.cs1', '36.dc1', '36.de1', '162.j1', '162.t1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 7, 39957619, 40320], 'label': '46656.ir.18.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712417
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fw1', '72.fx1', '108.bd1'], 'contains': ['432.gm1', '432.gt1', '432.gw1', '432.ik1', '432.im1', '432.lc1', '432.lp1', '648.ia1', '648.im1', '648.io1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 268280812800, 6227827207, 104], 'label': '46656.ir.216.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.in1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.in1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712418
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fx1', '108.x1'], 'contains': ['432.gp1', '432.gs1', '432.gy1', '432.is1', '432.it1', '432.lv1', '432.mf1', '648.ib1', '648.in1', '648.io1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.216.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '216.io1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.io1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712419
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fy1', '72.ga1', '108.bd1'], 'contains': ['432.ft1', '432.gb1', '432.gt1', '432.hf1', '432.hr1', '432.jg1', '432.jt1', '648.id1', '648.ip1', '648.iq1', '648.ir1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 1174320, 6227827200, 435], 'label': '46656.ir.216.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.ip1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ip1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712420
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fy1', '72.fz1'], 'contains': ['432.fu1', '432.ge1', '432.gu1', '432.hi1', '432.hs1', '432.jj1', '432.ju1', '648.ie1', '648.ip1', '648.ir1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 268280812904, 6227827200, 1174645], 'label': '46656.ir.216.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '216.iq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iq1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712421
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fy1', '72.gb1', '108.g1'], 'contains': ['432.fv1', '432.gh1', '432.gv1', '432.hl1', '432.ht1', '432.jl1', '432.jv1', '648.if1', '648.ip1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 6227827200, 104, 1174645], 'label': '46656.ir.216.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.ir1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ir1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712422
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '108.bo1', '108.eh1', '108.fh1'], 'contains': ['432.jw1', '648.ik1', '648.is1', '864.br1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 174452060430, 6227827200], 'label': '46656.ir.216.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.is1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.is1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 216712423
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fz1', '72.ga1', '72.gb1', '108.a1', '108.cg1', '108.fi1'], 'contains': ['432.gq1', '432.hg1', '432.hu1', '432.ka1', '432.kk1', '648.ip1', '648.it1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684835, 1174320, 1481684400, 6227827200], 'label': '46656.ir.216.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.it1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.it1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712424
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.fz1', '72.ga1', '108.ch1'], 'contains': ['432.gr1', '432.hn1', '432.hv1', '432.kb1', '432.kl1', '648.ir1', '648.it1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 6227827200, 270715783395], 'label': '46656.ir.216.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '216.iu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iu1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712425
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ga1', '108.x1', '108.ci1', '108.fj1'], 'contains': ['432.gs1', '432.ho1', '432.hw1', '432.kc1', '432.km1', '648.iq1', '648.it1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.216.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.iv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iv1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712426
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gc1', '108.bp1', '108.by1', '108.fj1'], 'contains': ['432.hw1', '432.kd1', '432.kv1', '648.iu1', '1944.fm1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 39366316080, 1174320, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.216.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.iw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iw1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712427
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '9.a1'], 'contains': ['36.bd1', '36.be1', '36.bh1', '36.cw1', '36.cy1', '36.db1', '36.dg1', '162.k1', '162.u1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6267381127, 499, 7, 40320], 'label': '46656.ir.18.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712428
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gc1', '72.gd1', '108.l1', '108.ce1', '108.fi1'], 'contains': ['432.hu1', '432.ke1', '432.kp1', '648.iu1', '1944.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40327, 39366316080, 1481684835, 1174320, 1481684400, 6227827200], 'label': '46656.ir.216.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '216.ix1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ix1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712429
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ge1', '72.gf1', '72.gg1', '108.l1', '108.cg1', '108.dq1'], 'contains': ['432.hu1', '432.kh1', '432.kq1', '648.iv1', '1944.fr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 6267381127, 1481684835, 1174320, 1481684400, 39957127], 'label': '46656.ir.216.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.iy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iy1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712430
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ge1', '72.gf1', '108.ch1'], 'contains': ['432.hv1', '432.ki1', '432.ks1', '648.iv1', '1944.ft1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 39957127, 270715783395], 'label': '46656.ir.216.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '216.iz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.iz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712431
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gf1', '108.bp1', '108.ci1', '108.cx1'], 'contains': ['432.hw1', '432.kj1', '432.kw1', '648.iv1', '1944.fs1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 269279866800, 39957127], 'label': '46656.ir.216.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ja1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ja1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712432
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gh1', '72.gi1', '108.cm1', '108.dq1', '108.fi1'], 'contains': ['432.hu1', '432.ko1', '432.kx1', '648.iw1', '1944.fu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 41050800, 1481684400, 6227827200], 'label': '46656.ir.216.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '216.jb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jb1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712433
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '72.gi1', '108.cp1', '108.cx1', '108.fj1'], 'contains': ['432.a1', '432.hw1', '432.ku1', '648.iw1', '1944.fv1'], 'core': '432.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.216.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.jc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jc1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712434
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1', '108.bm1'], 'contains': ['432.ic1', '432.mg1', '432.mh1', '648.ix1', '1944.fz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 1174327, 6267669018, 268280812800, 325, 355419187304], 'label': '46656.ir.216.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.o1', 'old_label': '216.jd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jd1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712435
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1', '108.bc1'], 'contains': ['432.is1', '432.mk1', '432.ml1', '648.iy1', '1944.fz1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 6267669018, 1481684400, 1174789, 269279866800], 'label': '46656.ir.216.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '216.je1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.je1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712436
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1', '108.o1', '108.bn1', '108.fl1'], 'contains': ['432.iu1', '432.iv1', '432.jd1', '648.ja1', '648.jc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 6267381127, 268280812800, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jf1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712437
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gk1', '108.u1', '108.bg1', '108.fl1'], 'contains': ['432.iu1', '432.iw1', '432.ix1', '432.le1', '432.ll1', '648.iz1', '648.jd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 268280812800, 1174320, 355419187304, 6227827207, 1174645], 'label': '46656.ir.216.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jg1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712438
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1', '2.e1'], 'contains': ['8.b1', '8.c1', '8.f1', '12.bb1', '12.bj1', '16.b1', '108.eh1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.d1', '2.e1'], 'normal_contains': ['8.b1', '8.c1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712439
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '9.a1'], 'contains': ['36.bd1', '36.bf1', '36.bg1', '36.cx1', '36.cz1', '36.df1', '36.dh1', '162.l1', '162.v1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6267381127, 7, 39957619, 40320], 'label': '46656.ir.18.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712440
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '108.u1', '108.bn1', '108.fb1'], 'contains': ['432.iu1', '432.iy1', '432.jc1', '648.jb1', '648.je1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 6227464327, 355419187304, 39957127, 1174645], 'label': '46656.ir.216.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jh1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712441
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '108.n1', '108.br1', '108.fl1'], 'contains': ['432.iv1', '432.ix1', '432.ja1', '648.jf1', '648.jm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 268280812800, 1174320, 355419187304, 6227827207, 1174645], 'label': '46656.ir.216.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ji1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ji1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216712442
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '108.o1', '108.br1', '108.fg1'], 'contains': ['432.iv1', '432.iz1', '432.jb1', '648.jg1', '648.jn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 40327, 268280812800, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jj1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712443
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '108.t1', '108.bj1', '108.fl1'], 'contains': ['432.iw1', '432.ja1', '432.jd1', '648.jh1', '648.jj1', '648.jk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 6267381127, 268280812800, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jk1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712444
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '108.u1', '108.bj1', '108.fg1'], 'contains': ['432.iw1', '432.jb1', '432.jc1', '648.ji1', '648.jl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 6267381120, 268280812800, 1174320, 355419187304, 1174645], 'label': '46656.ir.216.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jl1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712445
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '108.u1', '108.br1', '108.eb1'], 'contains': ['432.ix1', '432.iy1', '432.jb1', '648.jo1', '648.jp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 355419187304, 6227827207, 39957127, 1174645], 'label': '46656.ir.216.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jm1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712446
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '108.t1', '108.br1', '108.fb1'], 'contains': ['432.iy1', '432.iz1', '432.ja1', '648.jq1', '648.jr1', '648.js1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 1174320, 355419187304, 39957127, 1174645], 'label': '46656.ir.216.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jn1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712447
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gk1', '72.gl1', '108.g1'], 'contains': ['432.je1', '432.jl1', '432.jp1', '432.ky1', '432.kz1', '432.ld1', '432.ln1', '648.iz1', '648.ju1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 6227827207, 104, 1174645], 'label': '46656.ir.216.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.jo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jo1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712448
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '108.bo1', '108.ew1', '108.fk1'], 'contains': ['432.jw1', '648.jt1', '648.jv1', '864.dd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 174452060430, 6267744000], 'label': '46656.ir.216.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.jp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jp1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 216712449
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gk1', '72.go1', '108.bd1'], 'contains': ['432.jf1', '432.jg1', '432.jo1', '432.lc1', '432.lf1', '432.lw1', '432.lx1', '648.jd1', '648.ju1', '648.jw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 1174320, 6227827207, 435], 'label': '46656.ir.216.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '216.jq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jq1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712450
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '9.a1'], 'contains': ['36.d1', '36.f1', '36.j1', '36.k1', '36.bc1', '36.bd1', '36.bk1', '36.bl1', '36.bn1', '36.bo1', '36.bp1', '36.ct1', '36.di1', '36.dn1', '36.dq1', '54.x1', '162.o1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 7, 41051125, 1521641624], 'label': '46656.ir.18.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712451
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '108.bh1', '108.fh1', '108.fk1'], 'contains': ['432.jw1', '648.jx1', '648.jy1', '864.fh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 41051125, 39957224, 174452060430], 'label': '46656.ir.216.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.jr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jr1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216712452
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '108.bq1', '108.eh1', '108.fk1'], 'contains': ['432.jw1', '648.jz1', '648.ka1', '648.kb1', '864.eq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 174452060430, 6227827207], 'label': '46656.ir.216.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.js1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.js1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216712453
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '108.bq1', '108.ew1', '108.fh1'], 'contains': ['432.jw1', '648.kc1', '648.kd1', '648.ke1', '864.hg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 41051125, 39957224, 174452060430], 'label': '46656.ir.216.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.jt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jt1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216712454
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '108.bw1', '108.fb1', '108.fl1'], 'contains': ['432.iu1', '432.ja1', '432.jx1', '648.jt1', '648.kf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 41051125, 6267744000], 'label': '46656.ir.216.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.ju1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ju1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 216712455
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hg1', '108.bv1', '108.fg1', '108.fl1'], 'contains': ['432.iv1', '432.iw1', '432.jk1', '432.jn1', '432.jx1', '648.jy1', '648.kg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 41051125, 31697930984, 37885034880], 'label': '46656.ir.216.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jv1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712456
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1', '108.bx1', '108.eb1', '108.fl1'], 'contains': ['432.ix1', '432.jd1', '432.jx1', '648.kb1', '648.kh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 41051125, 6227827207], 'label': '46656.ir.216.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jw1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712457
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1', '108.bx1', '108.fb1', '108.fg1'], 'contains': ['432.iz1', '432.jc1', '432.jx1', '648.ke1', '648.ki1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 39957120, 41050800, 355459144424, 41051125], 'label': '46656.ir.216.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '216.jx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jx1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712458
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gl1', '72.go1', '108.a1', '108.cj1', '108.fm1'], 'contains': ['432.jy1', '432.ka1', '432.kg1', '432.lb1', '432.lh1', '648.ju1', '648.kj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.216.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.jy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jy1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712459
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gm1', '72.gp1', '108.l1', '108.cf1', '108.fm1'], 'contains': ['432.jy1', '432.ke1', '432.kq1', '648.kk1', '1944.gb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 40327], 'label': '46656.ir.216.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.jz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.jz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712460
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gn1', '72.gq1', '108.l1', '108.cj1', '108.dr1'], 'contains': ['432.jy1', '432.kh1', '432.kp1', '648.kl1', '1944.gc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6227464327, 39957127], 'label': '46656.ir.216.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.ka1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ka1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712461
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.e1', '36.g1', '36.u1', '36.v1', '36.y1', '36.z1', '36.be1', '36.bf1', '36.bn1', '36.dj1', '36.dk1', '54.r1', '162.x1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050800, 39957120, 39916800, 268280812800, 37885034880, 499, 7, 41051125, 31697930984], 'label': '46656.ir.18.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712462
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.go1', '108.x1', '108.ck1', '108.fn1'], 'contains': ['432.jz1', '432.kc1', '432.kf1', '432.lv1', '432.lz1', '648.jw1', '648.kj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.216.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712463
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gp1', '108.bp1', '108.bz1', '108.fn1'], 'contains': ['432.jz1', '432.kd1', '432.kw1', '648.kk1', '1944.gd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 39366316080, 6267381127, 1174320, 1481684400, 269279866800], 'label': '46656.ir.216.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kc1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712464
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gq1', '108.bp1', '108.ck1', '108.dl1'], 'contains': ['432.jz1', '432.kj1', '432.kv1', '648.kl1', '1944.gf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227464327, 269279866800, 39957127], 'label': '46656.ir.216.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kd1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712465
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gr1', '72.gs1', '72.gu1', '108.b1', '108.cg1', '108.fm1'], 'contains': ['432.ka1', '432.kn1', '432.kq1', '648.km1', '1944.gi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 1481684835, 1174320, 1481684400], 'label': '46656.ir.216.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.ke1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ke1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712466
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gt1', '72.gv1', '108.b1', '108.cj1', '108.fi1'], 'contains': ['432.ka1', '432.ko1', '432.kp1', '648.kn1', '1944.gj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 6267381120, 39366316080, 1481684835, 1174320, 1481684400], 'label': '46656.ir.216.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.kf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kf1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712467
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gr1', '72.gs1', '108.ch1'], 'contains': ['432.kb1', '432.kr1', '432.ks1', '648.km1', '1944.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 1174320, 1481684400, 270715783395], 'label': '46656.ir.216.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '216.kg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712468
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gs1', '108.z1', '108.ci1', '108.fn1'], 'contains': ['432.kc1', '432.kt1', '432.kw1', '648.km1', '1944.gk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 1174320, 1481684400, 269279866800], 'label': '46656.ir.216.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712469
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gt1', '108.z1', '108.ck1', '108.fj1'], 'contains': ['432.kc1', '432.ku1', '432.kv1', '648.kn1', '1944.gl1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 6267381120, 39366316080, 1174320, 1481684400, 269279866800], 'label': '46656.ir.216.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ki1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ki1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712470
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gw1', '108.bs1', '108.by1', '108.fn1'], 'contains': ['432.kd1', '432.kf1', '432.kt1', '648.ko1', '1944.gg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 39366316080, 1174320, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.216.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kj1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712471
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gx1', '108.bs1', '108.bz1', '108.fj1'], 'contains': ['432.kd1', '432.km1', '432.ku1', '648.kp1', '1944.gh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 40327, 39366316080, 1174320, 1481684400, 269279866800], 'label': '46656.ir.216.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kk1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712530
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cj1', '96.m1', '96.n1', '144.fk1'], 'contains': ['576.q1', '864.a1', '864.ci1'], 'core': '864.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [41091120, 462923481264, 39366316080, 1481684400, 269279866800], 'label': '46656.ir.288.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1', 'old_label': '288.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bj1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712472
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '9.a1'], 'contains': ['36.h1', '36.i1', '36.bg1', '36.bh1', '36.bn1', '36.dl1', '36.dm1', '162.q1', '162.y1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 7, 41051125, 6227827818, 1521641624], 'label': '46656.ir.18.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712473
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gw1', '72.gy1', '108.m1', '108.ce1', '108.fm1'], 'contains': ['432.ke1', '432.kg1', '432.kn1', '648.ko1', '1944.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40327, 39366316080, 1481684835, 1174320, 1481684400, 6227827207], 'label': '46656.ir.216.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '216.kl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kl1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712474
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gx1', '72.gz1', '108.m1', '108.cf1', '108.fi1'], 'contains': ['432.ke1', '432.kk1', '432.ko1', '648.kp1', '1944.go1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267381120, 40327, 39366316080, 1174320, 1481684400, 1481684504], 'label': '46656.ir.216.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.km1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.km1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712475
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ha1', '108.bs1', '108.ck1', '108.cx1'], 'contains': ['432.kf1', '432.kj1', '432.ku1', '648.kq1', '1944.gp1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 269279866800, 6227827207, 39957127], 'label': '46656.ir.216.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712476
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ha1', '72.hb1', '108.m1', '108.cj1', '108.dq1'], 'contains': ['432.kg1', '432.kh1', '432.ko1', '648.kq1', '1944.gq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6227827207, 39957127], 'label': '46656.ir.216.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.ko1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ko1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712477
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hc1', '72.hd1', '72.he1', '108.m1', '108.cg1', '108.dr1'], 'contains': ['432.kh1', '432.kk1', '432.kn1', '648.kr1', '1944.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504, 39957127], 'label': '46656.ir.216.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.kp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712478
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hc1', '72.hd1', '108.ch1'], 'contains': ['432.ki1', '432.kl1', '432.kr1', '648.kr1', '1944.gt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 39957127, 270715783395], 'label': '46656.ir.216.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '216.kq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kq1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712479
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hd1', '108.bs1', '108.ci1', '108.dl1'], 'contains': ['432.kj1', '432.km1', '432.kt1', '648.kr1', '1944.gs1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 269279866800, 39957127], 'label': '46656.ir.216.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kr1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712480
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hf1', '72.hj1', '108.cm1', '108.dr1', '108.fm1'], 'contains': ['432.jy1', '432.kn1', '432.kx1', '648.ks1', '1944.gu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 6267744000, 1521641624], 'label': '46656.ir.216.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '216.ks1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ks1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712481
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hg1', '72.hl1', '108.cl1', '108.fi1', '108.fm1'], 'contains': ['432.ji1', '432.jm1', '432.ka1', '432.ke1', '432.kx1', '648.kg1', '648.kt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 31697931315, 37885034880], 'label': '46656.ir.216.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.kt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kt1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712482
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hh1', '72.hm1', '108.cn1', '108.dq1', '108.fm1'], 'contains': ['432.kg1', '432.kq1', '432.kx1', '648.ku1', '1944.gz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 41050800, 1481684400, 6227827207], 'label': '46656.ir.216.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.ku1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ku1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712483
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '9.b1'], 'contains': ['36.a1', '36.bq1', '36.bu1', '36.bx1', '36.by1', '36.dp1', '36.ds1', '54.y1', '72.ck1', '486.h1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 623823424560, 1481684400, 39957120, 39916800, 6227827207, 7, 269279866800], 'label': '46656.ir.18.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712484
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hi1', '72.hp1', '108.cn1', '108.dr1', '108.fi1'], 'contains': ['432.kk1', '432.kp1', '432.kx1', '648.kv1', '1944.hc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 1521641955, 39957120, 41050800, 1481684400], 'label': '46656.ir.216.kv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '216.kv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kv1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712485
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '72.hj1', '108.cp1', '108.dl1', '108.fn1'], 'contains': ['432.a1', '432.jz1', '432.kt1', '648.ks1', '1944.hf1'], 'core': '432.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6267744000], 'label': '46656.ir.216.kw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.kw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kw1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712486
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hk1', '72.hl1', '108.co1', '108.fj1', '108.fn1'], 'contains': ['432.a1', '432.kc1', '432.kd1', '648.kt1'], 'core': '432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800], 'label': '46656.ir.216.kx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.kx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kx1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712487
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hm1', '72.hn1', '72.ho1', '108.cq1', '108.cx1', '108.fn1'], 'contains': ['432.a1', '432.kf1', '432.kw1', '648.ku1', '1944.hh1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.216.ky1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.ky1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ky1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712488
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '216.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hp1', '72.hq1', '72.hr1', '108.cq1', '108.dl1', '108.fj1'], 'contains': ['432.a1', '432.km1', '432.kv1', '648.kv1', '1944.hi1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 1481684400, 269279866800], 'label': '46656.ir.216.kz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '216.kz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.kz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712489
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '27.a1'], 'contains': ['486.h1', '486.i1', '486.j1', '486.s1', '486.t1', '486.u1', '486.v1', '729.a1', '972.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [43673374524, 37924992444, 499, 536532640560, 37924992000, 39916800, 2957880240], 'label': '46656.ir.243.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '243.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216712490
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '243.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1', '27.c1'], 'contains': ['486.b1', '486.c1', '486.d1', '486.e1', '486.f1', '486.g1', '486.k1', '486.l1', '486.n1', '486.o1', '486.p1', '486.q1', '486.r1', '486.w1', '486.x1', '729.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [34136928000, 31697931324, 39957120, 499, 39916800, 443609999724, 37885034880], 'label': '46656.ir.243.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '243.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712491
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1', '144.b1', '144.c1', '144.d1', '144.e1', '144.f1', '144.g1', '144.be1'], 'contains': ['576.l1', '864.b1', '864.c1', '864.d1', '864.e1', '864.f1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 39916800], 'label': '46656.ir.288.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '288.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1', 'subgroup_fusion': None, 'weyl_group': '32.25'}
  • id: 216712492
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '144.l1', '144.v1', '144.z1'], 'contains': ['576.a1', '864.d1', '864.g1', '864.h1', '864.i1', '864.l1', '864.m1', '864.m2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684725, 39366316080, 268280812800, 39916800, 104], 'label': '46656.ir.288.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '288.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712493
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '144.r1', '144.ba1', '144.bf1'], 'contains': ['576.b1', '864.b1', '864.h1', '864.i1', '864.j1', '864.m1', '864.m2', '864.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [268280812800, 325, 1481684504, 39916800, 37885034880], 'label': '46656.ir.288.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.u1', 'old_label': '288.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712494
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '9.b1'], 'contains': ['36.bq1', '36.bz1', '36.ca1', '54.z1', '72.cn1', '486.i1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [623823424560, 39957120, 39916800, 39366316080, 499, 2957558124, 41050800, 269279866800, 1481684400], 'label': '46656.ir.18.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712495
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '144.h1', '144.m1', '144.q1', '144.s1', '144.w1', '144.bb1', '144.bg1'], 'contains': ['576.c1', '864.c1', '864.g1', '864.j1', '864.l1', '864.n1', '864.o1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 39916800, 269279866800], 'label': '46656.ir.288.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '288.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
  • id: 216712496
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1', '144.i1', '144.k1', '144.n1', '144.o1', '144.x1', '144.y1', '144.bc1'], 'contains': ['576.k1', '864.f1', '864.g1', '864.h1', '864.k1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 39916800, 104], 'label': '46656.ir.288.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712497
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1', '144.j1', '144.p1', '144.t1', '144.u1', '144.bd1', '144.be1', '144.bh1'], 'contains': ['576.l1', '864.e1', '864.i1', '864.j1', '864.k1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 325, 39916800, 31658054504, 37885034880], 'label': '46656.ir.288.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '288.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712498
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cp1', '96.e1', '144.bi1', '144.bj1', '144.bk1', '144.bl1', '144.bm1', '144.bn1', '144.bo1'], 'contains': ['576.p1', '864.p1', '864.q1', '864.r1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.288.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '288.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712499
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.a1', '96.e1', '144.h1', '144.bp1', '144.bs1', '144.bt1', '144.bu1'], 'contains': ['576.c1', '864.p1', '864.s1', '864.t1', '864.u1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1481684835, 7, 1481684400, 269279866800], 'label': '46656.ir.288.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '288.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
  • id: 216712500
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.f1', '144.bq1', '144.br1', '144.bv1'], 'contains': ['576.e1', '864.q1', '864.u1', '864.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 7, 325, 641394472778, 270715782960], 'label': '46656.ir.288.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '288.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216712501
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.e1', '96.g1', '144.bw1'], 'contains': ['576.g1', '864.r1', '864.u1', '864.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [40323593624, 624190336641, 7, 40323593520, 269279866800], 'label': '46656.ir.288.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.n1', 'old_label': '288.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1', 'subgroup_fusion': None, 'weyl_group': '324.122'}
  • id: 216712502
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '144.i1', '144.bx1', '144.by1', '144.cd1', '144.cg1', '144.cj1', '144.cm1', '144.cp1', '144.cq1', '144.cr1', '144.cs1', '144.ct1', '144.cu1', '144.cv1', '144.cw1'], 'contains': ['576.k1', '864.s1', '864.x1', '864.y1', '864.z1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 325, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.288.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712503
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '144.b1', '144.j1', '144.bz1', '144.ce1', '144.ch1', '144.ci1', '144.ck1', '144.cx1', '144.cy1', '144.cz1', '144.da1', '144.db1', '144.dc1', '144.dd1', '144.de1'], 'contains': ['576.l1', '864.t1', '864.x1', '864.z1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.288.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '288.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1', 'subgroup_fusion': None, 'weyl_group': '288.936'}
  • id: 216712504
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '96.f1', '96.g1', '144.ca1', '144.cf1', '144.cl1', '144.df1', '144.dg1', '144.dh1', '144.di1'], 'contains': ['576.m1', '864.u1', '864.y1', '864.z1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 7, 325, 269279866800, 104], 'label': '46656.ir.288.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '288.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712505
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '9.b1'], 'contains': ['36.bq1', '36.cb1', '36.cc1', '54.ba1', '72.co1', '486.j1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 623823424560, 1481684400, 39957120, 39916800, 6227827818, 269279866800], 'label': '46656.ir.18.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712506
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1', '144.cb1', '144.cc1', '144.cn1', '144.dj1', '144.dk1', '144.dl1', '144.dm1'], 'contains': ['576.n1', '864.v1', '864.y1', '864.ba1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [300933848880, 7, 325, 382729979624, 461482882830], 'label': '46656.ir.288.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '288.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712507
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1', '144.co1', '144.dn1', '144.do1'], 'contains': ['576.o1', '864.w1', '864.y1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [300933848880, 7, 325, 382729979624, 176887030590], 'label': '46656.ir.288.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '288.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1', 'subgroup_fusion': None, 'weyl_group': '216.168'}
  • id: 216712508
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '144.k1', '144.bx1', '144.dp1', '144.dq1', '144.dr1', '144.ds1', '144.eo1'], 'contains': ['576.k1', '864.bb1', '864.bc1', '864.bd1', '864.be1', '864.bf1', '864.bg1', '864.bh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 6227827200, 104], 'label': '46656.ir.288.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216712509
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.h1', '144.l1', '144.ec1', '144.eh1'], 'contains': ['576.a1', '864.bc1', '864.bi1', '864.bn1', '864.bo1', '864.bs1', '864.bw1', '864.bw2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624, 268280812800, 40323593520, 6227827200, 34096648645], 'label': '46656.ir.288.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '288.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712510
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.h1', '144.dy1', '144.ei1', '144.ep1'], 'contains': ['576.b1', '864.be1', '864.bj1', '864.bm1', '864.bo1', '864.bt1', '864.bw1', '864.bw2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 1481684400, 6227827200, 355419187304, 269279867125], 'label': '46656.ir.288.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '288.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712511
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.h1', '96.i1', '144.m1', '144.bp1', '144.dx1', '144.dz1', '144.ed1', '144.ej1', '144.eq1'], 'contains': ['576.c1', '864.bb1', '864.bi1', '864.bj1', '864.bk1', '864.bs1', '864.bt1', '864.bu1', '864.bv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.288.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '288.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216712512
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.h1', '96.j1', '144.ek1'], 'contains': ['576.d1', '864.bd1', '864.bk1', '864.bm1', '864.bn1', '864.bo1', '864.bv1', '864.bw1', '864.bw2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [40323593624, 40323593520, 269279866800, 6227827200, 34096648645], 'label': '46656.ir.288.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '288.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712513
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '144.n1', '144.by1', '144.du1', '144.eb1', '144.ee1', '144.el1', '144.eo1'], 'contains': ['576.k1', '864.bf1', '864.bi1', '864.bm1', '864.bq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 40323593520, 6227827200], 'label': '46656.ir.288.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712514
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '144.c1', '144.bz1', '144.dv1', '144.ea1', '144.ef1', '144.em1', '144.er1'], 'contains': ['576.l1', '864.bh1', '864.bj1', '864.bn1', '864.bq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 6227827200], 'label': '46656.ir.288.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712515
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1', '96.k1', '144.ca1', '144.dw1', '144.en1'], 'contains': ['576.m1', '864.bg1', '864.bk1', '864.bo1', '864.bq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.288.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '288.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712516
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.j1', '6.k1'], 'contains': ['36.l1', '36.m1', '36.w1', '36.x1', '36.ba1', '36.bb1', '36.bj1', '36.bm1', '36.br1', '36.bs1', '36.bt1', '36.cd1', '36.ce1', '36.do1', '36.dr1', '54.x1', '54.y1', '162.r1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 7, 269279866800, 1521641624], 'label': '46656.ir.18.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '18.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216712517
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.k1', '144.cb1', '144.dt1', '144.eg1'], 'contains': ['576.n1', '864.bg1', '864.bl1', '864.bp1', '864.br1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [300933848880, 325, 6227827200, 382729979624, 461482882830], 'label': '46656.ir.288.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '288.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712518
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.i1', '96.j1', '96.k1', '144.bq1', '144.es1', '144.eu1'], 'contains': ['576.e1', '864.bk1', '864.bl1', '864.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [554365249658, 325, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.288.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '288.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216712519
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ez1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '96.i1', '144.bi1', '144.et1', '144.ev1'], 'contains': ['576.p1', '864.bu1', '864.bx1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 624302466480, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.288.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '288.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712520
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.i1', '96.j1', '144.ew1'], 'contains': ['576.r1', '864.bv1', '864.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [622713415418, 39366316405, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.288.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '288.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712521
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.l1', '144.cc1', '144.dt1', '144.ex1'], 'contains': ['576.n1', '864.by1', '864.bz1', '864.ca1', '864.cc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 300933848880, 325, 382729979624, 457175461950], 'label': '46656.ir.288.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '288.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712522
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.l1', '96.m1', '144.br1', '144.es1', '144.fc1'], 'contains': ['576.e1', '864.bz1', '864.cg1', '864.ch1', '864.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 641394472778, 270715782960], 'label': '46656.ir.288.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1', 'old_label': '288.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216712523
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.l1', '96.n1', '144.fd1'], 'contains': ['576.f1', '864.ca1', '864.cg1', '864.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [41091120, 39366316080, 722937560115, 269279866800, 104], 'label': '46656.ir.288.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bp1', 'old_label': '288.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bd1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712524
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '144.o1', '144.cd1', '144.dp1', '144.du1', '144.ez1', '144.fb1', '144.fe1'], 'contains': ['576.k1', '864.cb1', '864.cc1', '864.cd1', '864.ce1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 325, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.288.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.be1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216712525
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '144.d1', '144.p1', '144.ce1', '144.dv1', '144.ey1', '144.fa1', '144.ff1'], 'contains': ['576.l1', '864.cb1', '864.cd1', '864.cf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 268280812800, 325, 31658054504, 37885034880], 'label': '46656.ir.288.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '288.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216712526
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1', '96.l1', '144.cf1', '144.dw1', '144.fg1'], 'contains': ['576.m1', '864.cc1', '864.cd1', '864.cg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 269279866800, 104], 'label': '46656.ir.288.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '288.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216712527
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '9.b1'], 'contains': ['36.bx1', '36.bz1', '36.cb1', '54.bb1', '72.cl1', '486.s1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 623823424560, 1481684400, 39957120, 43673374524, 499, 2957558124, 269279866800], 'label': '46656.ir.18.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712528
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.b1', '96.m1', '96.n1', '144.q1', '144.bs1', '144.dx1', '144.fh1', '144.fi1'], 'contains': ['576.c1', '864.a1', '864.ce1', '864.cf1', '864.cg1'], 'core': '864.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.288.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '288.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216712529
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '96.m1', '144.bj1', '144.et1', '144.fj1'], 'contains': ['576.p1', '864.a1', '864.ch1'], 'core': '864.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.288.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '288.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bi1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712531
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1', '144.o1', '144.cg1', '144.eo1', '144.fl1', '144.fm1', '144.fp1', '144.fr1'], 'contains': ['576.k1', '864.cj1', '864.ck1', '864.cn1', '864.cp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 325, 1481684400, 1521641624], 'label': '46656.ir.288.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bk1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712532
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1', '144.p1', '144.be1', '144.ch1', '144.fn1', '144.fo1', '144.fq1', '144.gr1'], 'contains': ['576.l1', '864.cj1', '864.cl1', '864.cm1', '864.co1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 325, 1481684400, 1521641624], 'label': '46656.ir.288.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '288.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bl1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712533
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.o1', '144.bf1', '144.ep1', '144.fu1', '144.gb1', '144.ge1', '144.gh1', '144.gi1'], 'contains': ['576.b1', '864.cl1', '864.cn1', '864.cq1', '864.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [268280812800, 39957120, 325, 37885034880, 1521641624], 'label': '46656.ir.288.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '288.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bm1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712534
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.o1', '144.q1', '144.bg1', '144.bt1', '144.eq1', '144.ft1', '144.fv1', '144.fx1', '144.fz1', '144.gc1', '144.gf1', '144.gj1', '144.gk1', '144.gl1', '144.gm1', '144.gs1'], 'contains': ['576.c1', '864.ck1', '864.cm1', '864.cq1', '864.cr1', '864.cs1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 1481684400, 269279866800], 'label': '46656.ir.288.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '288.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bn1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 216712535
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.o1', '144.d1', '144.bh1', '144.ci1', '144.er1', '144.fs1', '144.fw1', '144.fy1', '144.ga1', '144.gd1', '144.gg1', '144.gn1', '144.go1', '144.gp1', '144.gq1', '144.gr1'], 'contains': ['576.l1', '864.co1', '864.cp1', '864.cq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 39957120, 325, 31697930984, 37885034880], 'label': '46656.ir.288.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '288.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bo1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216712536
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1', '144.k1', '144.cj1', '144.du1', '144.fl1', '144.gv1', '144.gw1', '144.gz1'], 'contains': ['576.k1', '864.ct1', '864.cu1', '864.cv1', '864.da1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 104, 6267744000], 'label': '46656.ir.288.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bp1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712537
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1', '144.c1', '144.ck1', '144.dv1', '144.fs1', '144.gu1', '144.gx1', '144.ha1'], 'contains': ['576.l1', '864.ct1', '864.cw1', '864.cz1', '864.dc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 6267744000], 'label': '46656.ir.288.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '288.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bq1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712538
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '9.b1'], 'contains': ['36.bx1', '36.ca1', '36.cc1', '54.bc1', '72.cm1', '486.t1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43673374524, 39917299, 39366316080, 39957120, 41050800, 2957558124, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.18.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712539
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1', '96.q1', '96.r1', '144.cl1', '144.dw1', '144.gy1'], 'contains': ['576.m1', '864.ct1', '864.cx1', '864.cy1', '864.db1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 325, 269279866800, 104, 6267744000], 'label': '46656.ir.288.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '288.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.br1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216712540
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.p1', '144.l1', '144.hd1', '144.hj1'], 'contains': ['576.a1', '864.cv1', '864.cy1', '864.cz1', '864.de1', '864.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [268280812800, 325, 1481684504, 40323593520, 6267744000], 'label': '46656.ir.288.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '288.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712541
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.p1', '96.s1', '144.m1', '144.bu1', '144.dx1', '144.ft1', '144.hb1', '144.he1', '144.hk1'], 'contains': ['576.c1', '864.cu1', '864.cw1', '864.cx1', '864.de1', '864.dh1', '864.di1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 269279866800, 6267744000], 'label': '46656.ir.288.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '288.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bt1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712542
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.q1', '96.s1', '144.bv1', '144.es1', '144.hg1'], 'contains': ['576.e1', '864.cx1', '864.df1', '864.dj1', '864.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 325, 641394472778, 270715782960, 6267744000], 'label': '46656.ir.288.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1', 'old_label': '288.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bu1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216712543
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.r1', '96.s1', '144.bw1'], 'contains': ['576.g1', '864.cx1', '864.dg1', '864.dk1', '864.dm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39366316080, 270715782960, 642871761921, 104, 6267744000], 'label': '46656.ir.288.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1', 'old_label': '288.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bv1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 216712544
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.q1', '144.hh1'], 'contains': ['576.i1', '864.cy1', '864.df1', '864.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [438489677070, 270715783064, 325, 388956924720, 6267744000], 'label': '46656.ir.288.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.ci1', 'old_label': '288.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bw1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712545
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.r1'], 'contains': ['576.j1', '864.cy1', '864.dg1', '864.dm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [299935198184, 455255499150, 39366316405, 388956924720, 6267744000], 'label': '46656.ir.288.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.r1', 'old_label': '288.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bx1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216712546
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1', '144.n1', '144.cm1', '144.dp1', '144.fl1', '144.hc1', '144.hf1', '144.hl1'], 'contains': ['576.k1', '864.da1', '864.db1', '864.dc1', '864.de1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 40323593520, 6267744000], 'label': '46656.ir.288.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.by1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216712547
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1', '144.cn1', '144.dt1', '144.hi1'], 'contains': ['576.n1', '864.db1', '864.dd1', '864.df1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [294706903784, 325, 174451657230, 388956924720, 6267744000], 'label': '46656.ir.288.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '288.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bz1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216712548
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.r1', '144.co1'], 'contains': ['576.o1', '864.db1', '864.dg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [455255499150, 294706903784, 325, 388956924720, 6267744000], 'label': '46656.ir.288.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '288.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ca1', 'subgroup_fusion': None, 'weyl_group': '216.53'}
  • id: 216712549
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.f1', '2.g1'], 'contains': ['8.b1', '8.d1', '8.g1', '12.bc1', '12.bx1', '16.d1', '108.ew1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.f1', '2.g1'], 'normal_contains': ['8.b1', '8.d1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712550
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '9.b1'], 'contains': ['36.by1', '36.bz1', '36.cc1', '54.bd1', '72.cq1', '486.u1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 623823424560, 1481684400, 2918003897, 39957120, 7, 269279866800], 'label': '46656.ir.18.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712551
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '96.s1', '144.bk1', '144.et1', '144.hm1'], 'contains': ['576.p1', '864.di1', '864.dj1', '864.dk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 623823424560, 6267744000], 'label': '46656.ir.288.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '288.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cb1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712552
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.t1', '144.r1', '144.dy1', '144.fu1'], 'contains': ['576.b1', '864.dn1', '864.do1', '864.dr1', '864.dt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 39366316080, 270715783064, 325, 1481684400], 'label': '46656.ir.288.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '288.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cc1', 'subgroup_fusion': None, 'weyl_group': '144.172'}
  • id: 216712553
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.t1', '144.h1', '144.s1', '144.dz1', '144.fh1', '144.fv1', '144.fx1', '144.hb1'], 'contains': ['576.c1', '864.dn1', '864.do1', '864.dp1', '864.dq1', '864.ds1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.288.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '288.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cd1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 216712554
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.t1', '144.b1', '144.t1', '144.ea1', '144.ey1', '144.fo1', '144.fw1', '144.gu1'], 'contains': ['576.l1', '864.dn1', '864.du1', '864.dv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 1481684400, 1481684504], 'label': '46656.ir.288.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '288.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ce1', 'subgroup_fusion': None, 'weyl_group': '288.936'}
  • id: 216712555
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.t1', '144.i1', '144.dq1', '144.eb1', '144.ez1', '144.fm1', '144.gv1', '144.hc1'], 'contains': ['576.k1', '864.dq1', '864.dt1', '864.dv1', '864.dw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 325, 104], 'label': '46656.ir.288.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cf1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712556
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.t1', '144.e1', '144.j1', '144.u1', '144.fa1', '144.fn1', '144.fo1', '144.fy1'], 'contains': ['576.l1', '864.dr1', '864.ds1', '864.du1', '864.dw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39916807, 268280812800, 325, 31658054504, 37885034880], 'label': '46656.ir.288.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '288.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cg1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712557
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.w1', '144.v1', '144.ec1', '144.hd1'], 'contains': ['576.a1', '864.dx1', '864.dy1', '864.eb1', '864.ee1', '864.eh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 1481684504, 6227827207], 'label': '46656.ir.288.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '288.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ch1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 216712558
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.u1', '96.v1', '96.w1', '144.w1', '144.bp1', '144.ed1', '144.fi1', '144.fz1', '144.hb1', '144.he1'], 'contains': ['576.c1', '864.dx1', '864.dy1', '864.dz1', '864.ea1', '864.ec1', '864.ed1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.288.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '288.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ci1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712559
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.w1', '144.x1', '144.bx1', '144.ee1', '144.fb1', '144.fp1', '144.gv1', '144.hf1'], 'contains': ['576.k1', '864.dx1', '864.ei1', '864.ej1', '864.ek1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 6227827207, 104], 'label': '46656.ir.288.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cj1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712560
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hn1', '96.u1', '144.bi1', '144.fj1', '144.hm1'], 'contains': ['576.p1', '864.dz1', '864.el1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 624302466480, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.288.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '288.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ck1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712561
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '9.b1'], 'contains': ['36.by1', '36.ca1', '36.cb1', '54.be1', '72.cr1', '486.v1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 623823424560, 1481684400, 39957120, 6267668542, 7, 269279866800], 'label': '46656.ir.18.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712562
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ho1', '96.u1', '96.v1', '144.fk1'], 'contains': ['576.q1', '864.dz1', '864.em1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 6227827207, 463289990028], 'label': '46656.ir.288.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fk1', 'old_label': '288.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cl1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712563
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.u1', '96.x1', '144.bq1', '144.fc1', '144.hg1'], 'contains': ['576.e1', '864.ed1', '864.ef1', '864.el1', '864.em1', '864.en1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624, 132379435521, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.288.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '288.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cm1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216712564
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.v1', '96.x1', '144.fd1'], 'contains': ['576.f1', '864.ed1', '864.eg1', '864.em1', '864.eo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [325, 40323593520, 269279866800, 6227827207, 463289990028], 'label': '46656.ir.288.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bs1', 'old_label': '288.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cn1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216712565
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.x1', '144.hh1'], 'contains': ['576.i1', '864.ee1', '864.ef1', '864.eg1', '864.en1', '864.eo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [300933848880, 270715783064, 325, 6227827207, 461482882830], 'label': '46656.ir.288.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hh1', 'old_label': '288.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.co1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712566
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.w1', '144.y1', '144.by1', '144.dr1', '144.fe1', '144.fp1', '144.gw1', '144.hc1'], 'contains': ['576.k1', '864.ea1', '864.eb1', '864.ei1', '864.ep1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 40323593520, 6227827207], 'label': '46656.ir.288.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cp1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712567
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.w1', '144.f1', '144.bz1', '144.ef1', '144.ff1', '144.ga1', '144.gu1', '144.gx1'], 'contains': ['576.l1', '864.ec1', '864.eh1', '864.ek1', '864.ep1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.288.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cq1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712568
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.w1', '96.x1', '144.ca1', '144.fg1', '144.gy1'], 'contains': ['576.m1', '864.ed1', '864.ee1', '864.ej1', '864.ep1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.288.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '288.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cr1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712569
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.x1', '144.cb1', '144.ex1', '144.hi1'], 'contains': ['576.n1', '864.ef1', '864.eg1', '864.ej1', '864.eq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [300933848880, 325, 382729979624, 6227827207, 461482882830], 'label': '46656.ir.288.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '288.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cs1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712570
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.y1', '144.z1', '144.ec1', '144.hj1'], 'contains': ['576.a1', '864.er1', '864.es1', '864.et1', '864.ew1', '864.ex1', '864.ex2', '864.fc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [301891126320, 325, 1481684400, 31658054504, 39957127], 'label': '46656.ir.288.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '288.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ct1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216712571
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.y1', '144.r1', '144.ba1', '144.gb1'], 'contains': ['576.b1', '864.es1', '864.et1', '864.eu1', '864.ex1', '864.ex2', '864.ey1', '864.fa1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 270715783064, 325, 1481684400, 39957127], 'label': '46656.ir.288.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '288.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cu1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216712572
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '9.a1'], 'contains': ['36.cp1', '36.cs1', '36.ct1', '36.db1', '36.dh1', '36.dj1', '36.dl1', '162.z1', '162.bd1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 499, 7, 41051125, 1521641624], 'label': '46656.ir.18.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712573
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.y1', '144.s1', '144.bb1', '144.bt1', '144.ed1', '144.fh1', '144.gc1', '144.hk1'], 'contains': ['576.c1', '864.er1', '864.eu1', '864.ew1', '864.ey1', '864.ez1', '864.fb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 269279866800, 39957127], 'label': '46656.ir.288.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '288.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cv1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216712574
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1', '144.bc1', '144.cg1', '144.dr1', '144.ee1', '144.ez1', '144.gz1', '144.hl1'], 'contains': ['576.k1', '864.er1', '864.es1', '864.ev1', '864.fe1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 325, 1481684400, 1481684504, 39957127], 'label': '46656.ir.288.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cw1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712575
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1', '144.e1', '144.t1', '144.bd1', '144.ch1', '144.fa1', '144.fq1', '144.gd1'], 'contains': ['576.l1', '864.et1', '864.eu1', '864.ev1', '864.fd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 39957127], 'label': '46656.ir.288.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '288.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cx1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712576
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.y1', '144.g1', '144.u1', '144.ci1', '144.ef1', '144.ey1', '144.fq1', '144.ha1', '144.hn1', '144.ho1'], 'contains': ['576.l1', '864.fa1', '864.fb1', '864.fc1', '864.fd1', '864.fe1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 325, 31658054504, 39957127, 37885034880], 'label': '46656.ir.288.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '288.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cy1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712577
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.z1', '96.ba1', '96.bb1', '144.br1', '144.eu1', '144.hg1'], 'contains': ['576.e1', '864.ff1', '864.fi1', '864.fj1', '864.fo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593624, 132379435521, 40323593520, 269279866800, 41091127], 'label': '46656.ir.288.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '288.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cz1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216712578
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bb1', '144.hh1'], 'contains': ['576.i1', '864.ff1', '864.fj1', '864.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [300933848880, 270715783064, 325, 438010715790, 41091127], 'label': '46656.ir.288.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hh1', 'old_label': '288.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.da1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216712579
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bb1', '144.cc1', '144.eg1', '144.hi1'], 'contains': ['576.n1', '864.ff1', '864.fg1', '864.fh1', '864.fv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [300933848880, 325, 382729979624, 457175461950, 41091127], 'label': '46656.ir.288.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '288.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.db1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712580
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hk1', '96.z1', '144.bj1', '144.ev1', '144.hm1'], 'contains': ['576.p1', '864.fi1', '864.ga1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 623823424560, 41091127], 'label': '46656.ir.288.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '288.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dc1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712581
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.z1', '96.ba1', '144.ew1'], 'contains': ['576.r1', '864.fi1', '864.gb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1481684725, 39366316080, 622713012218, 270715782960, 41091127], 'label': '46656.ir.288.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ew1', 'old_label': '288.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dd1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712582
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '144.z1', '144.eh1', '144.hd1'], 'contains': ['576.a1', '864.fk1', '864.fl1', '864.fm1', '864.fp1', '864.fq1', '864.fs1', '864.ft1', '864.fx1', '864.fy1', '864.fy2', '864.gc1', '864.gd1', '864.gd2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316405, 269279866800, 31658054504, 37885034880, 41091127], 'label': '46656.ir.288.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '288.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.de1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216712583
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '9.a1'], 'contains': ['36.cq1', '36.cr1', '36.ct1', '36.df1', '36.dg1', '36.dk1', '36.dm1', '162.ba1', '162.be1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 7, 41051125, 39917299, 1521641624], 'label': '46656.ir.18.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712584
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '144.ba1', '144.ei1', '144.fu1'], 'contains': ['576.b1', '864.fl1', '864.fm1', '864.fn1', '864.fr1', '864.ft1', '864.fy1', '864.fy2', '864.fz1', '864.gd1', '864.gd2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [268280812800, 39366316405, 31658054504, 37885034880, 41091127], 'label': '46656.ir.288.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '288.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.df1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216712585
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '96.z1', '144.bb1', '144.bs1', '144.ej1', '144.fv1', '144.he1'], 'contains': ['576.c1', '864.fk1', '864.fn1', '864.fo1', '864.fx1', '864.fz1', '864.ga1', '864.gb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 269279866800, 41091127], 'label': '46656.ir.288.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '288.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dg1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216712586
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '96.ba1', '144.ek1'], 'contains': ['576.d1', '864.fo1', '864.fp1', '864.fr1', '864.fs1', '864.ft1', '864.gb1', '864.gc1', '864.gd1', '864.gd2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1481684725, 39366316080, 269279866800, 104, 41091127], 'label': '46656.ir.288.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bn1', 'old_label': '288.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dh1', 'subgroup_fusion': None, 'weyl_group': '972.460'}
  • id: 216712587
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1', '144.bc1', '144.cd1', '144.ds1', '144.el1', '144.fm1', '144.gw1', '144.hf1'], 'contains': ['576.k1', '864.fk1', '864.fl1', '864.fp1', '864.fr1', '864.fu1', '864.fv1', '864.fw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [325, 269279866800, 31658054504, 37885034880, 41091127], 'label': '46656.ir.288.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.di1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712588
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1', '144.g1', '144.bd1', '144.ce1', '144.em1', '144.fn1', '144.fw1', '144.gx1'], 'contains': ['576.l1', '864.fm1', '864.fn1', '864.fs1', '864.fu1', '864.fw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 325, 31658054504, 37885034880, 41091127], 'label': '46656.ir.288.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '288.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dj1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712589
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1', '96.bb1', '144.cf1', '144.en1', '144.gy1'], 'contains': ['576.m1', '864.fo1', '864.fq1', '864.ft1', '864.fv1', '864.fw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 325, 269279866800, 104, 41091127], 'label': '46656.ir.288.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '288.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dk1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216712590
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bg1', '144.v1', '144.eh1', '144.hj1'], 'contains': ['576.a1', '864.ge1', '864.gi1', '864.gj1', '864.gl1', '864.gt1', '864.gt2', '864.gv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 1481684725, 39366316080, 268280812800, 104], 'label': '46656.ir.288.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '288.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dl1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216712591
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bg1', '144.dy1', '144.ei1', '144.ge1'], 'contains': ['576.b1', '864.gf1', '864.gh1', '864.gj1', '864.gm1', '864.gt1', '864.gt2', '864.hb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 39366316080, 270715783064, 325, 1481684400], 'label': '46656.ir.288.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fz1', 'old_label': '288.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dm1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216712592
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bc1', '96.bd1', '96.bg1', '144.w1', '144.bu1', '144.dz1', '144.ej1', '144.fi1', '144.gf1', '144.hk1'], 'contains': ['576.c1', '864.ge1', '864.gf1', '864.gg1', '864.gl1', '864.gm1', '864.gn1', '864.go1', '864.gu1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684835, 1481684400, 269279866800], 'label': '46656.ir.288.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '288.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dn1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216712593
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.be1', '96.bf1', '96.bg1', '144.ek1'], 'contains': ['576.d1', '864.gg1', '864.gh1', '864.gi1', '864.gj1', '864.go1', '864.gt1', '864.gt2', '864.gw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 1481684725, 39366316080, 269279866800, 104], 'label': '46656.ir.288.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ek1', 'old_label': '288.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.do1', 'subgroup_fusion': None, 'weyl_group': '108.44'}
  • id: 216712594
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '9.a1'], 'contains': ['36.cw1', '36.cz1', '36.da1', '36.de1', '36.di1', '36.dj1', '36.dm1', '162.bb1', '162.bf1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 499, 7, 41051125, 1521641624], 'label': '46656.ir.18.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712595
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bc1', '96.be1', '96.bh1', '144.bv1', '144.eu1', '144.fc1'], 'contains': ['576.e1', '864.gg1', '864.gp1', '864.gq1', '864.gx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 39366316080, 270715782960, 623711294721, 104], 'label': '46656.ir.288.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '288.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dp1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216712596
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bd1', '96.bf1', '96.bh1', '144.fd1'], 'contains': ['576.f1', '864.gg1', '864.gq1', '864.gy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 39366316080, 188938194828, 325, 269279866800], 'label': '46656.ir.288.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fd1', 'old_label': '288.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dq1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216712597
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bc1', '96.bf1', '96.bi1', '144.bw1'], 'contains': ['576.g1', '864.gg1', '864.gr1', '864.gs1', '864.gz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 39366316080, 622713012218, 325, 270715782960], 'label': '46656.ir.288.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bw1', 'old_label': '288.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dr1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 216712598
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bd1', '96.be1', '96.bf1', '96.bi1'], 'contains': ['576.h1', '864.gg1', '864.gs1', '864.ha1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [6267744007, 39366316080, 456583967628, 325, 269279866800], 'label': '46656.ir.288.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ds1', 'old_label': '288.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ds1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 216712599
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1', '144.x1', '144.cj1', '144.dq1', '144.el1', '144.fe1', '144.fr1', '144.hl1'], 'contains': ['576.k1', '864.ge1', '864.gh1', '864.gk1', '864.hd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 325, 104], 'label': '46656.ir.288.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '288.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dt1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712600
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1', '144.f1', '144.ck1', '144.ea1', '144.em1', '144.ff1', '144.gg1', '144.ha1'], 'contains': ['576.l1', '864.gf1', '864.gi1', '864.gk1', '864.hf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 325, 1481684400, 1481684504], 'label': '46656.ir.288.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '288.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.du1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712601
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1', '96.bh1', '96.bi1', '144.cl1', '144.en1', '144.fg1'], 'contains': ['576.m1', '864.gg1', '864.gj1', '864.gk1', '864.he1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 325, 269279866800, 104], 'label': '46656.ir.288.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '288.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dv1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216712602
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hq1', '96.bc1', '144.bk1', '144.ev1', '144.fj1'], 'contains': ['576.p1', '864.gn1', '864.gp1', '864.gr1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.288.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '288.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dw1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712603
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hr1', '96.bc1', '96.bd1', '144.fk1'], 'contains': ['576.q1', '864.gn1', '864.gq1', '864.gs1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 462923481264, 39366316080, 1481684400, 269279866800], 'label': '46656.ir.288.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fk1', 'old_label': '288.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dx1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712604
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bc1', '96.be1', '144.ew1'], 'contains': ['576.r1', '864.go1', '864.gp1', '864.gs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 1481684725, 39366316080, 622713012218, 270715782960], 'label': '46656.ir.288.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ew1', 'old_label': '288.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dy1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216712605
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '9.a1'], 'contains': ['36.cx1', '36.cy1', '36.dc1', '36.dd1', '36.di1', '36.dk1', '36.dl1', '162.bc1', '162.bg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 7, 41051125, 6227827818, 1521641624], 'label': '46656.ir.18.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216712606
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bc1', '96.bf1'], 'contains': ['576.s1', '864.go1', '864.gq1', '864.gr1', '864.gs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684504, 270715782960, 623711294721], 'label': '46656.ir.288.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.dz1', 'old_label': '288.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dz1', 'subgroup_fusion': None, 'weyl_group': '162.19'}
  • id: 216712607
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bd1', '96.be1', '96.bf1'], 'contains': ['576.t1', '864.go1', '864.gq1', '864.gs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [6267744007, 1481684725, 39366316080, 188938194828, 269279866800], 'label': '46656.ir.288.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea1', 'old_label': '288.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ea1', 'subgroup_fusion': None, 'weyl_group': '162.19'}
  • id: 216712608
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ea2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.bd1', '96.be1', '96.bf1'], 'contains': ['576.t2', '864.go1', '864.gq1', '864.gs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1152, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684504, 722937560115, 269279866800], 'label': '46656.ir.288.ea2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ea2', 'old_label': '288.ea2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ea2', 'subgroup_fusion': None, 'weyl_group': '162.19'}
  • id: 216712609
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1', '144.y1', '144.cm1', '144.ds1', '144.eb1', '144.fb1', '144.fr1', '144.gz1'], 'contains': ['576.k1', '864.gu1', '864.gv1', '864.gw1', '864.hb1', '864.hd1', '864.he1', '864.hf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 325, 40323593520], 'label': '46656.ir.288.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.eb1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216712610
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1', '144.cn1', '144.eg1', '144.ex1'], 'contains': ['576.n1', '864.gx1', '864.gy1', '864.hc1', '864.he1', '864.hg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267744007, 294706903784, 325, 174451657230, 388956924720], 'label': '46656.ir.288.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '288.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ec1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216712611
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '288.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bi1', '144.co1'], 'contains': ['576.o1', '864.gz1', '864.ha1', '864.he1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6267744007, 455255499150, 294706903784, 325, 388956924720], 'label': '46656.ir.288.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '288.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ed1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216712612
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '108.v1', '162.a1'], 'contains': ['648.a1', '648.c1', '648.e1', '648.ee1', '648.ef1', '648.fz1', '648.ga1', '972.a1', '972.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [499, 1481684400, 443130957804, 269279866800, 40320, 1481684844], 'label': '46656.ir.324.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '324.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712613
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '108.w1', '162.a1'], 'contains': ['648.a1', '648.e1', '648.f1', '648.eg1', '648.eh1', '648.gb1', '648.gc1', '972.b1', '972.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41051299, 1481684400, 443130957804, 269279866800, 40320, 1481684844], 'label': '46656.ir.324.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '324.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712614
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.x1', '162.a1', '162.b1', '162.w1'], 'contains': ['648.a1', '648.b1', '648.v1', '648.y1', '648.bg1', '648.dy1', '648.en1', '648.fj1', '648.in1', '648.it1', '648.kj1', '972.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 39916800, 6227827207], 'label': '46656.ir.324.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712615
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '108.y1', '162.a1', '162.c1', '162.x1'], 'contains': ['648.b1', '648.c1', '648.f1', '648.eu1', '648.ev1', '648.fk1', '648.fm1', '972.f1', '972.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 499, 1134000, 37885034880], 'label': '46656.ir.324.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712616
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['1944.dc1', '1944.fb1', '1944.fc1', '1944.dd1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1', '12.w1', '12.ba1'], 'contains': ['48.d1', '48.g1', '48.k1', '72.ch1', '72.ci1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 41051125, 269279866800, 1521641624], 'label': '46656.ir.24.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['48.d1', '96.b1', '216.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '46656.ir', 'quotient_action_image': '24.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216712617
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1', '108.z1', '162.c1', '162.d1', '162.w1'], 'contains': ['648.b1', '648.bh1', '648.bi1', '648.fl1', '648.fo1', '648.km1', '648.kn1', '2916.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400, 39916800], 'label': '46656.ir.324.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712618
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '108.ba1', '162.b1', '162.d1', '162.x1'], 'contains': ['648.b1', '648.d1', '648.ew1', '648.fn1', '648.fq1', '972.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 41051299, 1134000, 37885034880], 'label': '46656.ir.324.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712619
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '108.bb1', '162.a1', '162.d1', '162.y1'], 'contains': ['648.b1', '648.e1', '648.ex1', '648.fp1', '648.fr1', '972.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 39916800, 6227827818], 'label': '46656.ir.324.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712620
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1', '108.bc1', '162.b1', '162.c1', '162.y1'], 'contains': ['648.b1', '648.bk1', '648.fs1', '648.ft1', '648.iy1', '2916.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 39916800, 6267381738], 'label': '46656.ir.324.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712621
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.g1', '108.bd1'], 'contains': ['648.g1', '648.h1', '648.j1', '648.q1', '648.u1', '648.x1', '648.be1', '648.go1', '648.gr1', '648.gs1', '648.gw1', '648.hz1', '648.im1', '648.ip1', '648.ju1', '972.e1', '972.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 39916800, 6227827207, 435], 'label': '46656.ir.324.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '324.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712622
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1', '108.e1', '108.be1', '162.e1'], 'contains': ['648.k1', '648.m1', '648.o1', '648.ha1', '648.hb1', '648.hu1', '648.hv1', '2916.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916800, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.324.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '324.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216712623
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1', '108.f1', '108.bf1', '162.e1'], 'contains': ['648.k1', '648.o1', '648.p1', '648.hc1', '648.hd1', '648.hw1', '648.hx1', '2916.b1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174819, 39916800, 6227827207, 7, 104, 325], 'label': '46656.ir.324.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216712624
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1', '108.bg1', '162.e1', '162.f1', '162.o1'], 'contains': ['648.k1', '648.l1', '648.s1', '648.t1', '648.ba1', '648.gz1', '648.he1', '648.hi1', '648.hy1', '648.if1', '648.iz1', '972.j1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 6227827207, 7, 104], 'label': '46656.ir.324.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712625
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.h1', '108.j1', '108.bi1', '162.e1', '162.g1', '162.p1'], 'contains': ['648.l1', '648.m1', '648.p1', '648.hf1', '648.hg1', '648.hj1', '648.hl1', '2916.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 499, 7, 325, 39957224, 1134000], 'label': '46656.ir.324.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.m1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216712626
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1', '108.bj1', '162.g1', '162.h1', '162.o1'], 'contains': ['648.l1', '648.bb1', '648.bc1', '648.hk1', '648.hn1', '648.jk1', '648.jl1', '972.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381127, 7, 1174320, 39916800, 104, 1174645], 'label': '46656.ir.324.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.n1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712627
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['1944.gw1', '1944.hd1', '1944.he1', '1944.fy1', '1944.ha1', '1944.hb1'], 'conjugacy_class_count': 1, 'contained_in': ['8.k1', '12.g1', '12.bd1'], 'contains': ['48.a1', '48.b1', '48.c1', '72.dy1', '72.ec1', '72.eg1', '216.eb1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 499, 7, 325, 269279866800], 'label': '46656.ir.24.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['48.a1', '48.b1', '48.c1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '46656.ir', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712628
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.i1', '108.bk1', '162.f1', '162.h1', '162.p1'], 'contains': ['648.l1', '648.n1', '648.hg1', '648.hm1', '648.hp1', '2916.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41051299, 7, 325, 39957224, 1134000], 'label': '46656.ir.324.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.o1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712629
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1', '108.bl1', '162.e1', '162.h1', '162.q1'], 'contains': ['648.l1', '648.o1', '648.hh1', '648.ho1', '648.hq1', '2916.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 7, 6227827818, 104], 'label': '46656.ir.324.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.p1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712630
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1', '108.bm1', '162.f1', '162.g1', '162.q1'], 'contains': ['648.l1', '648.bj1', '648.hr1', '648.hs1', '648.ix1', '2916.h1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 7, 6267381738, 104], 'label': '46656.ir.324.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.q1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712631
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1', '108.bn1', '162.o1'], 'contains': ['648.t1', '648.z1', '648.bc1', '648.ig1', '648.ij1', '648.ja1', '648.jb1', '972.l1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381127, 1174320, 39916800, 39957127, 104, 1174645], 'label': '46656.ir.324.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.r1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712632
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.l1', '108.bp1', '162.w1'], 'contains': ['648.y1', '648.bf1', '648.bi1', '648.iu1', '648.iv1', '648.kk1', '648.kl1', '2916.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 39916800, 39957127], 'label': '46656.ir.324.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.s1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712633
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1', '108.br1', '162.o1'], 'contains': ['648.z1', '648.ba1', '648.bb1', '648.jm1', '648.jn1', '648.jp1', '648.js1', '972.m1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916800, 1174645, 1174320, 6227827207, 39957127, 104], 'label': '46656.ir.324.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.t1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712634
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1', '108.bs1', '162.w1'], 'contains': ['648.bf1', '648.bg1', '648.bh1', '648.ko1', '648.kp1', '648.kq1', '648.kr1', '2916.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 39916800, 6227827207, 39957127], 'label': '46656.ir.324.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.u1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712635
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ba1', '108.n1', '162.r1'], 'contains': ['648.bm1', '648.bo1', '648.bw1', '648.gp1', '648.gu1', '648.ic1', '648.jf1', '972.n1', '972.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 268280812800, 7, 1174320, 40320, 6227827207], 'label': '46656.ir.324.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.v1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216712636
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bb1', '108.o1', '162.r1'], 'contains': ['648.bm1', '648.bs1', '648.by1', '648.gt1', '648.gv1', '648.jc1', '648.jg1', '972.o1', '972.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 6267381127, 268280812800, 7, 1174320, 40320], 'label': '46656.ir.324.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.w1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712637
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1', '108.n1', '162.i1', '162.j1', '162.o1'], 'contains': ['648.bn1', '648.bq1', '648.bx1', '648.he1', '648.hk1', '648.ig1', '648.jm1', '972.t1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 7, 104, 40320], 'label': '46656.ir.324.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.x1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712638
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.a1', '12.b1', '12.c1', '12.bj1', '12.bx1', '12.by1', '12.bz1'], 'contains': ['48.d1', '48.r1', '48.by1', '72.cy1', '72.fc1'], 'core': '24.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.24.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': ['8.b1', '12.a1', '12.b1', '12.c1'], 'normal_contains': ['48.d1', '96.a1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712639
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '108.o1', '162.k1', '162.l1', '162.o1'], 'contains': ['648.bn1', '648.br1', '648.ca1', '648.hi1', '648.hn1', '648.ja1', '648.jn1', '972.u1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6267381127, 7, 104, 40320], 'label': '46656.ir.324.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.y1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712640
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.p1', '108.bt1', '162.i1', '162.k1', '162.p1'], 'contains': ['648.m1', '648.n1', '648.bn1', '648.hj1', '648.hm1', '2916.m1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 499, 7, 325, 39957224, 39916800], 'label': '46656.ir.324.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.z1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712641
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.q1', '108.bu1', '162.j1', '162.l1', '162.p1'], 'contains': ['648.n1', '648.p1', '648.bn1', '648.hl1', '648.hp1', '2916.n1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41051299, 7, 325, 39957224, 39916800], 'label': '46656.ir.324.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ba1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712642
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '108.r1', '162.i1', '162.l1', '162.q1'], 'contains': ['648.bn1', '648.ho1', '648.hr1', '2916.o1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 7, 6227827818, 104, 40320], 'label': '46656.ir.324.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bb1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712643
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '108.s1', '162.j1', '162.k1', '162.q1'], 'contains': ['648.bn1', '648.hq1', '648.hs1', '2916.p1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 7, 6267381738, 104, 40320], 'label': '46656.ir.324.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bc1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712644
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bj1', '108.t1', '162.r1'], 'contains': ['648.bo1', '648.bt1', '648.by1', '648.id1', '648.ih1', '648.jh1', '648.jq1', '972.v1', '972.w1', '972.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 355419187304, 40320, 39957127], 'label': '46656.ir.324.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713128
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1', '216.ct1', '216.en1', '216.je1'], 'contains': ['864.ez1', '1296.lw1', '3888.go1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174789, 269279866800, 6227752218], 'label': '46656.ir.432.mk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '432.mk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mk1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712645
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bi1', '108.t1'], 'contains': ['648.bp1', '648.bu1', '648.bz1', '648.ie1', '648.ii1', '648.jj1', '648.jr1', '972.v1', '972.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [268281987445, 6267381127, 1174320, 355419187304, 40320, 39957127], 'label': '46656.ir.324.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '324.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.be1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 216712646
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bk1', '108.t1', '162.o1'], 'contains': ['648.bq1', '648.bv1', '648.ca1', '648.if1', '648.ij1', '648.jk1', '648.js1', '972.v1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6267381127, 39957127, 104, 40320], 'label': '46656.ir.324.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bf1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712647
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1', '108.u1', '162.o1'], 'contains': ['648.br1', '648.bv1', '648.bx1', '648.iz1', '648.jb1', '648.jl1', '648.jp1', '972.y1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 39957127, 104, 40320], 'label': '46656.ir.324.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bg1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712648
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bm1', '108.u1', '162.r1'], 'contains': ['648.bs1', '648.bt1', '648.bw1', '648.jd1', '648.je1', '648.ji1', '648.jo1', '972.y1', '972.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 268280812800, 1174320, 40320, 6227827207, 39957127], 'label': '46656.ir.324.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712649
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['1944.dc1', '1944.fc1', '1944.fb1', '1944.dd1'], 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '12.a1', '12.ca1', '12.cc1'], 'contains': ['48.d1', '48.bv1', '48.bw1', '72.hg1', '72.hl1'], 'core': '24.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.24.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': ['8.e1', '12.a1'], 'normal_contains': ['48.d1', '96.c1'], 'normalizer': '1.a1', 'old_label': '24.d1', 'projective_image': '46656.ir', 'quotient_action_image': '24.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712650
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '108.v1', '162.m1'], 'contains': ['648.cb1', '648.cf1', '648.cg1', '648.ds1', '648.dt1', '648.fv1', '648.fw1', '972.a1', '972.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 499, 443130957804, 270715782960, 40320, 37885034880], 'label': '46656.ir.324.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712651
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '108.w1', '162.m1'], 'contains': ['648.cb1', '648.ch1', '648.ci1', '648.du1', '648.dv1', '648.fx1', '648.fy1', '972.b1', '972.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41051299, 270715782960, 742619410284, 40320, 37885034880], 'label': '46656.ir.324.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712652
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1', '108.v1', '162.m1'], 'contains': ['648.cc1', '648.cf1', '648.ch1', '648.ea1', '648.eb1', '648.gf1', '648.gg1', '972.c1', '972.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [31658054844, 499, 443130957804, 269279866800, 40320, 37885034880], 'label': '46656.ir.324.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '324.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712653
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '108.w1', '162.m1'], 'contains': ['648.cc1', '648.cg1', '648.ci1', '648.ec1', '648.ed1', '648.gh1', '648.gi1', '972.d1', '972.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41051299, 443130957804, 269279866800, 40320, 37885034880], 'label': '46656.ir.324.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712654
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.x1', '108.bd1', '162.m1'], 'contains': ['648.cb1', '648.cc1', '648.cd1', '648.cq1', '648.ct1', '648.cu1', '648.dd1', '648.dr1', '648.dx1', '648.em1', '648.fa1', '648.ib1', '648.io1', '648.iq1', '648.jw1', '972.e1', '972.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 1174320, 39916800, 6227827207], 'label': '46656.ir.324.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712655
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '108.y1', '162.m1'], 'contains': ['648.cd1', '648.cf1', '648.ci1', '648.eq1', '648.er1', '648.fb1', '648.fc1', '972.h1', '972.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 39957120, 499, 1481684400, 1521641964, 1134000], 'label': '46656.ir.324.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712656
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '108.bb1', '162.m1'], 'contains': ['648.cd1', '648.cg1', '648.ch1', '648.es1', '648.et1', '648.fd1', '648.fe1', '972.i1', '972.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 268280812800, 1174320, 39916800, 6227827818], 'label': '46656.ir.324.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712657
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1', '108.y1', '162.x1'], 'contains': ['648.ce1', '648.cj1', '648.cm1', '648.eu1', '648.ew1', '648.ff1', '648.fg1', '972.f1', '972.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 499, 1481684400, 1521641964, 1134000], 'label': '46656.ir.324.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712658
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '108.ba1', '162.x1'], 'contains': ['648.ce1', '648.ck1', '648.cl1', '648.ev1', '648.ew1', '648.fh1', '648.fi1', '972.g1', '972.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 41051299, 1481684400, 1521641964, 1134000], 'label': '46656.ir.324.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712659
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bd1', '108.bg1', '162.r1'], 'contains': ['648.cn1', '648.co1', '648.cp1', '648.cs1', '648.cz1', '648.gm1', '648.gp1', '648.gt1', '648.ia1', '648.id1', '648.jd1', '972.j1', '972.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 268280812800, 7, 1174320, 39916800, 6227827207], 'label': '46656.ir.324.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.br1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712660
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['11664.b1', '11664.e1', '11664.bj1', '11664.s1', '11664.r1', '11664.x1', '11664.bk1', '11664.u1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1', '2.f1'], 'contains': ['8.b1', '12.b1', '16.e1', '36.bz1', '108.ex1'], 'core': '4.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 499, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': ['2.b1', '2.d1', '2.f1'], 'normal_contains': ['8.b1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '46656.ir', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712661
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.e1', '12.f1'], 'contains': ['48.e1', '48.f1', '48.i1', '48.o1', '48.s1', '48.bg1', '48.cg1', '72.d1', '72.q1', '72.s1', '72.t1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 6227827207, 7, 325, 269279866800], 'label': '46656.ir.24.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216712662
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.v1', '108.bh1', '162.n1'], 'contains': ['648.cv1', '648.gx1', '648.jx1', '972.bd1', '972.bj1', '1296.el1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 7, 39957224, 39916800, 132379435521, 1520467200], 'label': '46656.ir.324.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '324.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bs1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216712663
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.m1', '108.bj1', '162.r1'], 'contains': ['648.co1', '648.da1', '648.db1', '648.gu1', '648.gv1', '648.jh1', '648.ji1', '972.k1', '972.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381127, 268280812800, 7, 1174320, 39916800, 355419187304], 'label': '46656.ir.324.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712664
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bh1', '108.bv1', '162.o1', '162.p1', '162.q1'], 'contains': ['648.l1', '648.z1', '648.bn1', '648.bv1', '648.cx1', '648.ht1', '648.jy1', '972.bj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 7, 41051125, 39957224, 39916800], 'label': '46656.ir.324.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '324.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712665
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bo1', '108.bo1', '108.bw1', '162.o1'], 'contains': ['648.t1', '648.bb1', '648.bq1', '648.br1', '648.cx1', '648.ik1', '648.jt1', '972.bk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 39916800, 6227827200], 'label': '46656.ir.324.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bv1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216712666
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.w1', '108.bn1', '162.r1'], 'contains': ['648.cs1', '648.cy1', '648.db1', '648.ic1', '648.ih1', '648.jc1', '648.je1', '972.l1', '972.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 6267381127, 268280812800, 1174320, 39916800, 39957127], 'label': '46656.ir.324.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712667
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.x1', '108.bo1', '162.n1'], 'contains': ['648.cv1', '648.is1', '648.jv1', '972.bk1', '972.bm1', '1296.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2957880565, 655807627898, 39916800, 6227827200, 2957880240, 31697930880], 'label': '46656.ir.324.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '324.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bx1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216712668
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.y1', '108.bq1', '162.n1'], 'contains': ['648.cv1', '648.jz1', '648.kc1', '972.bn1', '972.bo1', '972.bp1', '1296.hp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2957880565, 655807627898, 39916800, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.324.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '324.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.by1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216712669
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.z1', '108.bq1'], 'contains': ['648.cw1', '648.ka1', '648.kd1', '972.bn1', '972.bp1', '1296.hq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [174564190515, 39957120, 41050800, 39957224, 39916800, 6227827207], 'label': '46656.ir.324.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.bz1', 'old_label': '324.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bz1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 216712670
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bp1', '108.bq1', '108.bx1', '162.o1'], 'contains': ['648.ba1', '648.bc1', '648.bx1', '648.ca1', '648.cx1', '648.kb1', '648.ke1', '972.bn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 39916800, 6227827207], 'label': '46656.ir.324.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ca1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712671
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.x1', '108.br1', '162.r1'], 'contains': ['648.cy1', '648.cz1', '648.da1', '648.jf1', '648.jg1', '648.jo1', '648.jq1', '972.m1', '972.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 268280812800, 1174320, 39916800, 6227827207, 39957127], 'label': '46656.ir.324.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712672
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.f1', '12.g1', '12.h1', '12.i1', '12.j1', '12.k1'], 'contains': ['48.a1', '48.e1', '48.g1', '48.j1', '48.r1', '48.bq1', '48.bv1', '72.e1', '72.r1', '72.u1', '72.v1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 325, 1481684400, 269279866800, 1134000, 1521641624], 'label': '46656.ir.24.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712673
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '108.ca1', '162.x1'], 'contains': ['648.c1', '648.d1', '648.cj1', '648.ck1', '648.de1', '648.ff1', '648.fh1', '972.p1', '972.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 499, 1481684400, 1521641964, 39916800], 'label': '46656.ir.324.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712674
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '108.cb1', '162.x1'], 'contains': ['648.d1', '648.f1', '648.cl1', '648.cm1', '648.de1', '648.fg1', '648.fi1', '972.q1', '972.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 41051299, 1481684400, 1521641964, 39916800], 'label': '46656.ir.324.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '324.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712675
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.bv1', '108.cl1', '162.r1'], 'contains': ['648.i1', '648.bd1', '648.bm1', '648.bt1', '648.co1', '648.cy1', '648.df1', '648.dg1', '648.dj1', '648.gy1', '648.kg1', '972.bj1', '972.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39916800, 31697930984, 37885034880], 'label': '46656.ir.324.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712676
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bs1', '108.bw1', '162.r1'], 'contains': ['648.bo1', '648.bs1', '648.cs1', '648.da1', '648.dj1', '648.il1', '648.kf1', '972.bk1', '972.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [355459144755, 268280812800, 39957120, 41050800, 39916800, 6227827200], 'label': '46656.ir.324.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '324.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216712677
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bt1', '108.bx1', '162.r1'], 'contains': ['648.bw1', '648.by1', '648.cz1', '648.db1', '648.dj1', '648.kh1', '648.ki1', '972.bn1', '972.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 39916800, 6227827207], 'label': '46656.ir.324.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712678
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.by1', '108.ce1', '162.s1', '162.t1', '162.w1'], 'contains': ['648.dk1', '648.dl1', '648.do1', '648.en1', '648.fl1', '648.iu1', '648.ko1', '2916.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174320, 6227827207, 7, 40320], 'label': '46656.ir.324.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ch1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712679
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bz1', '108.cf1', '162.u1', '162.v1', '162.w1'], 'contains': ['648.dk1', '648.dm1', '648.dp1', '648.fj1', '648.fo1', '648.kk1', '648.kp1', '2916.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400, 40320], 'label': '46656.ir.324.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ci1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713129
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ml1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1', '216.ct1', '216.eo1', '216.je1'], 'contains': ['864.ez1', '1296.lx1', '3888.gp1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 6267669018, 1481684400, 1174789, 269279866800], 'label': '46656.ir.432.ml1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '432.ml1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ml1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712680
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1', '108.ca1', '162.s1', '162.u1', '162.x1'], 'contains': ['648.cj1', '648.cl1', '648.dk1', '648.fk1', '648.fn1', '972.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 499, 39916800, 37885034880], 'label': '46656.ir.324.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cj1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712681
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '108.cb1', '162.t1', '162.v1', '162.x1'], 'contains': ['648.ck1', '648.cm1', '648.dk1', '648.fm1', '648.fq1', '972.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 41051299, 39916800, 37885034880], 'label': '46656.ir.324.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ck1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712682
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1', '108.cc1', '162.s1', '162.v1', '162.y1'], 'contains': ['648.dk1', '648.fp1', '648.fs1', '2916.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 39366316080, 1174320, 1481684400, 6227827818, 40320], 'label': '46656.ir.324.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cl1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712683
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.g1', '12.p1'], 'contains': ['48.b1', '48.e1', '48.v1', '72.f1', '72.w1', '72.ba1', '216.bj1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 499, 7, 325, 269279866800], 'label': '46656.ir.24.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '1728.47045'}
  • id: 216712684
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1', '108.cd1', '162.t1', '162.u1', '162.y1'], 'contains': ['648.dk1', '648.fr1', '648.ft1', '2916.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [469, 39366316080, 1174320, 1481684400, 6267381738, 40320], 'label': '46656.ir.324.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cm1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712685
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cg1', '108.ch1', '108.ci1', '162.w1'], 'contains': ['648.dl1', '648.dn1', '648.dp1', '648.it1', '648.iv1', '648.km1', '648.kr1', '2916.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 40320, 39957127], 'label': '46656.ir.324.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712686
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cj1', '108.ck1', '162.w1'], 'contains': ['648.dm1', '648.dn1', '648.do1', '648.kj1', '648.kl1', '648.kn1', '648.kq1', '2916.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174320, 6227827207, 39957127, 40320], 'label': '46656.ir.324.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.co1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712687
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cl1', '108.co1', '162.w1', '162.x1', '162.y1'], 'contains': ['648.b1', '648.bf1', '648.ce1', '648.dc1', '648.de1', '648.di1', '648.dk1', '648.dn1', '648.dq1', '648.fu1', '648.kt1', '972.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 7, 39916800, 37885034880], 'label': '46656.ir.324.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cp1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712688
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cm1', '108.cp1', '162.w1'], 'contains': ['648.y1', '648.bh1', '648.dl1', '648.dm1', '648.dq1', '648.iw1', '648.ks1', '2916.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 6227827200], 'label': '46656.ir.324.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cq1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712689
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cn1', '108.cq1', '162.w1'], 'contains': ['648.bg1', '648.bi1', '648.do1', '648.dp1', '648.dq1', '648.ku1', '648.kv1', '2916.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 6227827207], 'label': '46656.ir.324.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cr1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712690
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cf1', '108.cr1', '162.m1'], 'contains': ['648.dr1', '648.ds1', '648.dv1', '648.eq1', '648.es1', '648.gf1', '648.gh1', '972.bw1', '972.by1', '972.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091120, 499, 270715782960, 742619410284, 37885034880], 'label': '46656.ir.324.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712691
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cg1', '108.cs1', '162.m1'], 'contains': ['648.dr1', '648.dt1', '648.du1', '648.er1', '648.et1', '648.gg1', '648.gi1', '972.bx1', '972.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091120, 41051299, 270715782960, 742619410284, 37885034880], 'label': '46656.ir.324.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ct1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712692
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ch1', '108.cy1'], 'contains': ['648.dw1', '648.ek1', '648.el1', '648.eo1', '648.ep1', '648.gj1', '648.gk1', '972.by1', '972.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 301891126320, 499, 655477406640, 444, 6227389164], 'label': '46656.ir.324.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '324.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712693
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ci1', '108.cr1', '162.m1'], 'contains': ['648.dx1', '648.ea1', '648.ed1', '648.eq1', '648.et1', '648.fv1', '648.fx1', '972.bw1', '972.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091120, 499, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.324.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712694
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '12.p1', '12.q1'], 'contains': ['48.e1', '48.v1', '48.x1', '72.g1', '72.bb1', '72.bc1', '216.bk1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 7, 39957619, 325, 40320, 269279866800], 'label': '46656.ir.24.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216712695
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cj1', '108.cs1', '162.m1'], 'contains': ['648.dx1', '648.eb1', '648.ec1', '648.er1', '648.es1', '648.fw1', '648.fy1', '972.bx1', '972.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091120, 41051299, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.324.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712696
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ck1', '108.cr1', '162.a1'], 'contains': ['648.dy1', '648.ee1', '648.eh1', '648.eu1', '648.ex1', '648.fz1', '648.gb1', '972.bz1', '972.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 499, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.324.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '324.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712697
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cl1', '108.cs1', '162.a1'], 'contains': ['648.dy1', '648.ef1', '648.eg1', '648.ev1', '648.ex1', '648.ga1', '648.gc1', '972.ca1', '972.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 41051299, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.324.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '324.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712698
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cm1', '108.cr1', '108.cy1'], 'contains': ['648.dz1', '648.ei1', '648.ej1', '648.ey1', '648.ez1', '648.gd1', '648.ge1', '972.by1', '972.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 443130957804, 444, 269279866800], 'label': '46656.ir.324.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '324.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.cz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712699
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '108.ct1', '162.m1'], 'contains': ['648.ds1', '648.du1', '648.ea1', '648.ec1', '648.em1', '648.fb1', '648.fd1', '972.cb1', '972.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41050800, 499, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.324.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.da1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712700
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.co1', '108.cu1', '162.m1'], 'contains': ['648.dt1', '648.dv1', '648.eb1', '648.ed1', '648.em1', '648.fc1', '648.fe1', '972.cd1', '972.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 40819, 41050800, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.324.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.db1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712701
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cp1', '108.ct1', '162.a1', '162.s1', '162.z1'], 'contains': ['648.ee1', '648.eg1', '648.en1', '648.fk1', '648.fp1', '972.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050800, 499, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.324.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dc1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712702
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cq1', '108.cu1', '162.a1', '162.t1', '162.ba1'], 'contains': ['648.ef1', '648.eh1', '648.en1', '648.fm1', '648.fr1', '972.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [40819, 41050800, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.324.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dd1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712703
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cr1', '108.cv1', '162.b1', '162.s1', '162.ba1'], 'contains': ['648.en1', '648.fn1', '648.fs1', '2916.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 41050800, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.324.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.de1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712704
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cs1', '108.cw1', '162.b1', '162.t1', '162.z1'], 'contains': ['648.en1', '648.fq1', '648.ft1', '2916.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 1481684400, 443130957804, 269279866800, 39957619, 1481684844], 'label': '46656.ir.324.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.df1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712705
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.e1', '12.j1'], 'contains': ['48.e1', '48.w1', '48.y1', '72.h1', '72.x1', '72.y1', '216.bl1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 7, 6227827818, 325, 269279866800], 'label': '46656.ir.24.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216712706
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cx1', '108.dq1', '162.w1', '162.z1', '162.ba1'], 'contains': ['648.en1', '648.fo1', '648.fu1', '648.iv1', '648.iw1', '648.kq1', '648.ku1', '2916.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 7, 1481684400, 6227827207], 'label': '46656.ir.324.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dg1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712707
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cu1', '108.cz1', '162.m1'], 'contains': ['648.fa1', '648.fb1', '648.fe1', '648.fv1', '648.fy1', '648.gf1', '648.gi1', '972.cm1', '972.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 137, 268280812800, 7, 1174320], 'label': '46656.ir.324.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712708
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1', '108.da1', '162.m1'], 'contains': ['648.fa1', '648.fc1', '648.fd1', '648.fw1', '648.fx1', '648.gg1', '648.gh1', '972.co1', '972.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 6227827342, 268280812800, 7, 1174320], 'label': '46656.ir.324.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '324.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.di1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216712709
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cw1', '108.cz1', '162.a1', '162.u1', '162.bb1'], 'contains': ['648.fj1', '648.fk1', '648.fr1', '648.fz1', '648.gc1', '972.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684537, 7, 1174320, 1481684400], 'label': '46656.ir.324.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dj1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712710
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cx1', '108.da1', '162.a1', '162.v1', '162.bc1'], 'contains': ['648.fj1', '648.fm1', '648.fp1', '648.ga1', '648.gb1', '972.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [43633820302, 6267744007, 39366316080, 7, 1174320, 1481684400], 'label': '46656.ir.324.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dk1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712711
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cy1', '108.db1', '162.b1', '162.u1', '162.bc1'], 'contains': ['648.fj1', '648.fn1', '648.ft1', '2916.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39366316080, 43673374222, 7, 1174320, 1481684400], 'label': '46656.ir.324.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dl1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712712
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cz1', '108.dc1', '162.b1', '162.v1', '162.bb1'], 'contains': ['648.fj1', '648.fq1', '648.fs1', '2916.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1521641657, 6267744007, 39366316080, 7, 1174320, 1481684400], 'label': '46656.ir.324.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dm1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712713
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.da1', '108.dd1', '162.c1', '162.s1', '162.bb1'], 'contains': ['648.fk1', '648.fl1', '648.fs1', '2916.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684537, 7, 1174320, 1481684400, 6227464327], 'label': '46656.ir.324.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712714
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.db1', '108.de1', '162.c1', '162.u1', '162.z1'], 'contains': ['648.fk1', '648.fo1', '648.ft1', '2916.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 499, 1481684400, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.324.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.do1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712715
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1', '108.df1', '162.c1', '162.t1', '162.bc1'], 'contains': ['648.fl1', '648.fm1', '648.ft1', '2916.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 43673374222, 7, 1174320, 1481684400, 6227464327], 'label': '46656.ir.324.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dp1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712716
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.g1', '12.q1'], 'contains': ['48.c1', '48.e1', '48.x1', '72.i1', '72.z1', '72.bd1', '216.bm1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 1134000, 39957619], 'label': '46656.ir.24.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712717
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dd1', '108.dg1', '162.d1', '162.s1', '162.bc1'], 'contains': ['648.fl1', '648.fn1', '648.fp1', '2916.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43633820302, 39366316080, 7, 1174320, 1481684400, 6227464327], 'label': '46656.ir.324.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '324.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dq1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712718
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.de1', '108.dh1', '162.d1', '162.t1', '162.bb1'], 'contains': ['648.fl1', '648.fq1', '648.fr1', '2916.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1521641657, 39366316080, 7, 1174320, 1481684400, 6227464327], 'label': '46656.ir.324.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dr1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712719
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.df1', '108.di1', '162.c1', '162.v1', '162.ba1'], 'contains': ['648.fm1', '648.fo1', '648.fs1', '2916.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [40819, 41050800, 1481684400, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.324.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ds1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712720
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dg1', '108.dj1', '162.d1', '162.u1', '162.ba1'], 'contains': ['648.fn1', '648.fo1', '648.fr1', '2916.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39917299, 41050800, 1481684400, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.324.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dt1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712721
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dh1', '108.dk1', '162.d1', '162.v1', '162.z1'], 'contains': ['648.fo1', '648.fp1', '648.fq1', '2916.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 1481684400, 269279866800, 443609999724, 39957619, 1481684844], 'label': '46656.ir.324.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.du1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712722
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dl1', '108.dr1', '162.w1', '162.bb1', '162.bc1'], 'contains': ['648.fj1', '648.fl1', '648.fu1', '648.kl1', '648.kr1', '648.ks1', '648.kv1', '2916.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 7, 1481684400], 'label': '46656.ir.324.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dv1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712723
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dj1', '108.dm1', '162.x1', '162.z1', '162.bb1'], 'contains': ['648.ff1', '648.fi1', '648.fk1', '648.fq1', '648.fu1', '972.dg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 41050800, 499, 37885034880], 'label': '46656.ir.324.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dw1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712724
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dk1', '108.dn1', '162.x1', '162.ba1', '162.bc1'], 'contains': ['648.fg1', '648.fh1', '648.fm1', '648.fn1', '648.fu1', '972.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39917299, 31697931324, 268280812800, 39957120, 41050800, 37885034880], 'label': '46656.ir.324.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dx1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712725
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1', '108.do1', '162.y1', '162.z1', '162.bc1'], 'contains': ['648.fp1', '648.ft1', '648.fu1', '2916.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [469, 39366316080, 39957120, 41050800, 1481684400, 6227827818], 'label': '46656.ir.324.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dy1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712726
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dm1', '108.dp1', '162.y1', '162.ba1', '162.bb1'], 'contains': ['648.fr1', '648.fs1', '648.fu1', '2916.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 1481684400, 39957120, 6267744618], 'label': '46656.ir.324.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.dz1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712727
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1'], 'contains': ['48.f1', '48.i1', '48.j1', '48.bh1', '48.bi1', '48.ch1', '48.cj1', '72.j1', '72.be1', '72.bf1', '72.bg1', '72.bh1'], 'core': '96.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684504, 1481684400, 39916800, 6227827207, 325, 269279866800], 'label': '46656.ir.24.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216712728
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cd1', '108.eb1', '162.r1'], 'contains': ['648.gp1', '648.gv1', '648.gy1', '648.ih1', '648.il1', '648.jo1', '648.kh1', '972.cf1', '972.dk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355459144755, 268280812800, 39957120, 41050800, 7, 6227827207], 'label': '46656.ir.324.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ea1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712729
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.bb1', '108.eh1', '162.n1'], 'contains': ['648.gx1', '648.is1', '648.jz1', '972.cl1', '972.dk1', '1296.ek1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [7, 641394472778, 269202528325, 299859033600, 269202528000, 6227827207], 'label': '46656.ir.324.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '324.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eb1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216712730
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.bc1', '108.ew1', '162.n1'], 'contains': ['648.gx1', '648.jv1', '648.kc1', '972.da1', '972.dl1', '1296.ew1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 7, 39957224, 93536397441], 'label': '46656.ir.324.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '324.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ec1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216712731
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ce1', '108.fb1', '162.r1'], 'contains': ['648.gt1', '648.gu1', '648.gy1', '648.je1', '648.jq1', '648.kf1', '648.ki1', '972.df1', '972.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 268280812800, 39957120, 41050800, 7, 355459144424], 'label': '46656.ir.324.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ed1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712732
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ds1', '108.du1', '108.dv1', '108.ec1', '108.ed1', '162.e1'], 'contains': ['648.gz1', '648.ha1', '648.hd1', '648.hf1', '648.hh1', '648.hu1', '648.hw1', '2916.v1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.324.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ee1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216712733
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dt1', '108.dw1', '108.ee1', '162.e1'], 'contains': ['648.gz1', '648.hb1', '648.hc1', '648.hg1', '648.hh1', '648.hv1', '648.hx1', '2916.w1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174819, 41091120, 6227827207, 7, 104, 325], 'label': '46656.ir.324.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '324.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ef1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216712734
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dx1', '108.ef1', '162.e1', '162.i1', '162.bd1'], 'contains': ['648.ha1', '648.hc1', '648.he1', '648.hj1', '648.ho1', '2916.x1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 499, 7, 104], 'label': '46656.ir.324.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eg1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712735
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dz1', '108.eg1', '162.e1', '162.j1', '162.be1'], 'contains': ['648.hb1', '648.hd1', '648.he1', '648.hl1', '648.hq1', '2916.y1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 7, 39917299, 104], 'label': '46656.ir.324.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eh1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712736
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cr1', '108.dy1', '162.f1', '162.i1', '162.be1'], 'contains': ['648.he1', '648.hm1', '648.hr1', '2916.z1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 40819, 7, 104], 'label': '46656.ir.324.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ei1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712737
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cs1', '108.ea1', '162.f1', '162.j1', '162.bd1'], 'contains': ['648.he1', '648.hp1', '648.hs1', '2916.ba1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 7, 39957619, 104], 'label': '46656.ir.324.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ej1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216714496
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bz1', '864.ch1', '1296.ct1', '1296.go1', '1296.hy1'], 'contains': ['5184.q1', '7776.v1', '7776.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 301891126320, 655477406640], 'label': '46656.ir.2592.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '2592.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712738
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.l1', '12.w1'], 'contains': ['48.f1', '48.g1', '48.bf1', '48.bj1', '48.bu1', '72.k1', '72.bi1', '72.bj1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 39916800, 269279866800, 6227827200, 1174645], 'label': '46656.ir.24.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216712739
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ct1', '108.eb1', '108.eh1', '162.o1', '162.bd1', '162.be1'], 'contains': ['648.he1', '648.hn1', '648.ht1', '648.ij1', '648.ik1', '648.jp1', '648.kb1', '972.dk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 7, 41051125, 39957224, 6227827207], 'label': '46656.ir.324.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ek1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712740
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ei1', '108.eu1', '162.e1', '162.k1', '162.bf1'], 'contains': ['648.hi1', '648.hj1', '648.hq1', '648.hu1', '648.hx1', '2916.bc1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 1174645, 1174320, 499, 7, 104], 'label': '46656.ir.324.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.el1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712741
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ek1', '108.ev1', '162.e1', '162.l1', '162.bg1'], 'contains': ['648.hi1', '648.hl1', '648.ho1', '648.hv1', '648.hw1', '2916.bd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 7, 1174320, 6227827818, 104, 1174645], 'label': '46656.ir.324.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.em1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712742
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cy1', '108.ej1', '162.f1', '162.k1', '162.bg1'], 'contains': ['648.hi1', '648.hm1', '648.hs1', '2916.be1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 7, 1174320, 6267381738, 104, 1174645], 'label': '46656.ir.324.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.en1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712743
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cz1', '108.el1', '162.f1', '162.l1', '162.bf1'], 'contains': ['648.hi1', '648.hp1', '648.hr1', '2916.bf1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 1174645, 1174320, 7, 39957619, 104], 'label': '46656.ir.324.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eo1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712744
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.da1', '108.em1', '162.g1', '162.i1', '162.bf1'], 'contains': ['648.hj1', '648.hk1', '648.hr1', '2916.bg1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 499, 7, 104, 6227464327], 'label': '46656.ir.324.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ep1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712745
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.db1', '108.en1', '162.g1', '162.k1', '162.bd1'], 'contains': ['648.hj1', '648.hn1', '648.hs1', '2916.bh1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6267381127, 499, 7, 104], 'label': '46656.ir.324.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eq1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712746
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dc1', '108.ep1', '162.g1', '162.j1', '162.bg1'], 'contains': ['648.hk1', '648.hl1', '648.hs1', '2916.bi1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [7, 1174320, 6227464327, 6267381738, 104, 1174645], 'label': '46656.ir.324.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.er1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712747
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dd1', '108.eo1', '162.h1', '162.i1', '162.bg1'], 'contains': ['648.hk1', '648.hm1', '648.ho1', '2916.bj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 1174320, 6227464327, 6227827818, 104, 1174645], 'label': '46656.ir.324.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '324.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.es1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712748
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.de1', '108.eq1', '162.h1', '162.j1', '162.bf1'], 'contains': ['648.hk1', '648.hp1', '648.hq1', '2916.bk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 7, 39957619, 104, 6227464327], 'label': '46656.ir.324.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.et1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712749
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.l1', '12.m1'], 'contains': ['48.g1', '48.h1', '48.bq1', '48.bw1', '48.by1', '72.l1', '72.bk1', '72.bm1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 325, 1481684400, 269279866800, 1134000, 1521641624], 'label': '46656.ir.24.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712750
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.df1', '108.es1', '162.g1', '162.l1', '162.be1'], 'contains': ['648.hl1', '648.hn1', '648.hr1', '2916.bl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39917299, 6267381127, 7, 1174320, 104, 1174645], 'label': '46656.ir.324.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.eu1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712751
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dg1', '108.er1', '162.h1', '162.k1', '162.be1'], 'contains': ['648.hm1', '648.hn1', '648.hq1', '2916.bm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [40819, 6267381127, 7, 1174320, 104, 1174645], 'label': '46656.ir.324.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ev1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712752
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dh1', '108.et1', '162.h1', '162.l1', '162.bd1'], 'contains': ['648.hn1', '648.ho1', '648.hp1', '2916.bn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6267381127, 7, 39957619, 104], 'label': '46656.ir.324.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ew1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712753
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.di1', '108.ew1', '108.fb1', '162.o1', '162.bf1', '162.bg1'], 'contains': ['648.hi1', '648.hk1', '648.ht1', '648.jb1', '648.js1', '648.jt1', '648.ke1', '972.dl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 7, 41051125, 39957224], 'label': '46656.ir.324.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ex1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712754
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ex1', '108.fc1', '162.p1', '162.bd1', '162.bf1'], 'contains': ['648.hj1', '648.hp1', '648.ht1', '2916.bp1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 499, 7, 41051125], 'label': '46656.ir.324.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '324.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ey1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712755
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ey1', '108.fd1', '162.p1', '162.be1', '162.bg1'], 'contains': ['648.hl1', '648.hm1', '648.ht1', '2916.bq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39957120, 41050800, 7, 41051125, 39957224], 'label': '46656.ir.324.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '324.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ez1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712756
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1', '108.ez1', '108.fe1', '162.q1', '162.bd1', '162.bg1'], 'contains': ['648.ho1', '648.hs1', '648.ht1', '2916.br1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 7, 41051125, 39957224, 6227827818], 'label': '46656.ir.324.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fa1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712757
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dm1', '108.fa1', '108.ff1', '162.q1', '162.be1', '162.bf1'], 'contains': ['648.hq1', '648.hr1', '648.ht1', '2916.bs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 6267744618, 7, 41051125], 'label': '46656.ir.324.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fb1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712758
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dn1', '108.fg1', '108.fh1', '162.o1'], 'contains': ['648.if1', '648.ig1', '648.ik1', '648.jl1', '648.jn1', '648.jy1', '648.ke1', '972.dm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 41051125, 39957224, 6227827200], 'label': '46656.ir.324.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fc1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712759
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.do1', '108.fg1', '162.r1'], 'contains': ['648.ic1', '648.id1', '648.il1', '648.jg1', '648.ji1', '648.kg1', '648.ki1', '972.dm1', '972.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 355459144755, 268280812800, 39957120, 41050800, 6227827200], 'label': '46656.ir.324.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712760
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.m1', '12.ba1'], 'contains': ['48.g1', '48.i1', '48.bt1', '48.bx1', '48.bz1', '72.m1', '72.bl1', '72.bn1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6227827207, 269279866800], 'label': '46656.ir.24.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712761
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.cb1', '108.fh1', '162.n1'], 'contains': ['648.is1', '648.jx1', '648.kc1', '972.dm1', '972.do1', '1296.ha1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 2957880565, 655807627898, 6227827200, 2957880240, 31697930880], 'label': '46656.ir.324.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '324.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fe1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216712762
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fi1', '108.fj1', '162.w1'], 'contains': ['648.it1', '648.iu1', '648.iw1', '648.kn1', '648.kp1', '648.kt1', '648.kv1', '2916.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 6227827200], 'label': '46656.ir.324.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ff1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712763
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dq1', '108.fk1', '108.fl1', '162.o1'], 'contains': ['648.iz1', '648.ja1', '648.jk1', '648.jm1', '648.jt1', '648.jy1', '648.kb1', '972.dp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 41051125, 39957224, 6227827207], 'label': '46656.ir.324.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fg1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216712764
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.cd1', '108.fk1', '162.n1'], 'contains': ['648.jv1', '648.jx1', '648.jz1', '972.dp1', '972.dq1', '1296.lj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 2957880565, 655807627898, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.324.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '324.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fh1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216712765
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dr1', '108.fl1', '162.r1'], 'contains': ['648.jc1', '648.jd1', '648.jf1', '648.jh1', '648.kf1', '648.kg1', '648.kh1', '972.dp1', '972.dr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 355459144424, 6227827207], 'label': '46656.ir.324.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '324.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216712766
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '324.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fm1', '108.fn1', '162.w1'], 'contains': ['648.kj1', '648.kk1', '648.km1', '648.ko1', '648.ks1', '648.kt1', '648.ku1', '2916.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 6227827207], 'label': '46656.ir.324.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '324.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.fj1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216712767
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['108.ec1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '144.gs1', '144.gt1', '216.a1', '216.ep1', '216.jc1', '216.kw1', '216.kx1', '216.ky1', '216.kz1'], 'contains': ['864.cs1', '1296.kn1'], 'core': '432.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800], 'label': '46656.ir.432.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': ['48.d1', '144.a1', '216.a1'], 'normal_contains': ['1728.a1'], 'normalizer': '1.a1', 'old_label': '432.a1', 'projective_image': '46656.ir', 'quotient_action_image': '12.4', 'quotient_action_kernel': '36.9', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712768
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.b1', '144.h1', '216.b1', '216.c1', '216.cu1'], 'contains': ['864.c1', '864.t1', '864.dn1', '1296.b1', '1296.c1', '1296.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 1481684504, 39916800], 'label': '46656.ir.432.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216712769
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '144.j1', '216.f1', '216.h1', '216.i1', '216.j1', '216.k1', '216.bb1', '216.cv1'], 'contains': ['864.e1', '864.x1', '864.du1', '1296.c1', '1296.e1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7, 325, 39916800, 31658054504, 37885034880], 'label': '46656.ir.432.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712770
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '144.i1', '216.d1', '216.e1', '216.g1', '216.l1', '216.m1', '216.n1', '216.o1'], 'contains': ['864.f1', '864.z1', '864.dv1', '1296.d1', '1296.e1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 7, 325, 39916800, 104], 'label': '46656.ir.432.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712771
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['11664.e1', '11664.s1', '11664.b1', '11664.bj1', '11664.x1', '11664.u1', '11664.r1', '11664.bk1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.e1', '2.g1'], 'contains': ['8.b1', '12.c1', '16.g1', '36.ca1', '108.ey1'], 'core': '4.g1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 7, 41051125, 39917299, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.e1', '2.g1'], 'normal_contains': ['8.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '46656.ir', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712772
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.m1', '12.w1'], 'contains': ['48.g1', '48.ca1', '48.cb1', '72.n1', '72.bo1', '216.cj1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 39916800, 269279866800, 1174645], 'label': '46656.ir.24.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216712773
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '144.k1', '216.d1', '216.p1', '216.t1'], 'contains': ['864.f1', '864.bh1', '864.ct1', '1296.f1', '1296.g1', '1296.h1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 325, 39916800, 6227827200, 104], 'label': '46656.ir.432.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216712774
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '144.m1', '216.b1', '216.q1', '216.u1'], 'contains': ['864.c1', '864.bj1', '864.cw1', '1296.f1', '1296.i1', '1296.j1', '1296.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 39916800, 6227827200], 'label': '46656.ir.432.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '432.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712775
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.c1', '144.l1', '216.r1'], 'contains': ['864.d1', '864.bn1', '864.cz1', '1296.g1', '1296.i1', '1296.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593624, 39916800, 40323593520, 6227827200, 34096648645], 'label': '46656.ir.432.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '432.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712776
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1', '144.n1', '216.e1', '216.s1', '216.t1'], 'contains': ['864.f1', '864.bq1', '864.dc1', '1296.h1', '1296.i1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 325, 39916800, 40323593520, 6227827200], 'label': '46656.ir.432.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712777
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '144.p1', '216.f1', '216.v1', '216.cz1'], 'contains': ['864.e1', '864.cb1', '864.co1', '1296.l1', '1296.m1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 325, 1134000, 31697930984, 37885034880], 'label': '46656.ir.432.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '432.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712778
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1', '144.o1', '216.g1', '216.t1', '216.w1'], 'contains': ['864.f1', '864.cd1', '864.cp1', '1296.l1', '1296.n1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 39957120, 325, 39957224, 1134000], 'label': '46656.ir.432.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712779
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.d1', '144.q1', '216.c1', '216.u1', '216.x1', '216.y1', '216.z1', '216.ba1', '216.dp1'], 'contains': ['864.c1', '864.cf1', '864.cq1', '1296.m1', '1296.n1', '1296.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [268280812800, 39957120, 31697931315, 1134000, 37885034880], 'label': '46656.ir.432.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '432.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712780
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.e1', '144.r1', '216.cw1'], 'contains': ['864.b1', '864.dr1', '864.et1', '1296.p1', '1296.q1', '1296.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1481684400, 355419187304, 40320, 39957127, 269279867125], 'label': '46656.ir.432.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '432.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216712781
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.e1', '144.s1', '216.x1', '216.cu1', '216.cx1'], 'contains': ['864.c1', '864.ds1', '864.eu1', '1296.p1', '1296.q1', '1296.r1', '1296.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1481684835, 1481684400, 269279866800, 40320, 39957127], 'label': '46656.ir.432.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712782
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1', '144.t1', '216.v1', '216.bb1', '216.cy1'], 'contains': ['864.e1', '864.du1', '864.ev1', '1296.p1', '1296.u1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [325, 1481684400, 1481684504, 40320, 39957127], 'label': '46656.ir.432.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '432.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712783
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.l1', '12.ba1'], 'contains': ['48.g1', '48.cc1', '48.cd1', '72.o1', '72.bp1', '216.ck1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 39916800, 269279866800, 1174645], 'label': '46656.ir.24.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712784
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1', '144.u1', '216.v1', '216.be1', '216.cv1'], 'contains': ['864.e1', '864.dw1', '864.fd1', '1296.s1', '1296.t1', '1296.u1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 325, 355419187304, 40320, 39957127], 'label': '46656.ir.432.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712785
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.f1', '144.w1', '216.b1', '216.q1', '216.y1'], 'contains': ['864.c1', '864.ec1', '864.gf1', '1296.v1', '1296.w1', '1296.x1', '1296.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 39916800, 6227827207], 'label': '46656.ir.432.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.p1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712786
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.f1', '144.v1', '216.r1'], 'contains': ['864.d1', '864.eh1', '864.gi1', '1296.v1', '1296.x1', '1296.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1481684725, 39366316080, 39916800, 6227827207, 104], 'label': '46656.ir.432.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '432.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.q1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216712787
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1', '144.x1', '216.d1', '216.s1', '216.w1'], 'contains': ['864.f1', '864.ek1', '864.gk1', '1296.v1', '1296.ba1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 325, 39916800, 6227827207, 104], 'label': '46656.ir.432.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.r1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712788
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1', '144.y1', '216.e1', '216.p1', '216.w1'], 'contains': ['864.f1', '864.ep1', '864.hf1', '1296.y1', '1296.z1', '1296.ba1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 325, 39916800, 40323593520, 6227827207], 'label': '46656.ir.432.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.s1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712789
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.g1', '144.ba1', '216.cw1'], 'contains': ['864.b1', '864.fa1', '864.fm1', '1296.bb1', '1296.bd1', '1296.be1', '1296.bg1', '1296.bj1', '1296.bj2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [293708217925, 1134000, 355419187304, 39957127, 37885034880], 'label': '46656.ir.432.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '432.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.t1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712790
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.g1', '144.bb1', '216.c1', '216.q1', '216.cx1'], 'contains': ['864.c1', '864.fb1', '864.fn1', '1296.bb1', '1296.bc1', '1296.bg1', '1296.bh1', '1296.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 1134000, 31658054504, 39957127, 37885034880], 'label': '46656.ir.432.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.u1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712791
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.g1', '144.z1', '216.r1'], 'contains': ['864.d1', '864.fc1', '864.fs1', '1296.bc1', '1296.bd1', '1296.be1', '1296.bi1', '1296.bj1', '1296.bj2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [268280813125, 387037284480, 1134000, 355419187304, 39957127], 'label': '46656.ir.432.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '432.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.v1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712792
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1', '144.bd1', '216.f1', '216.be1', '216.cy1'], 'contains': ['864.e1', '864.fd1', '864.fu1', '1296.bb1', '1296.bd1', '1296.bf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [325, 1134000, 31658054504, 39957127, 37885034880], 'label': '46656.ir.432.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '432.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.w1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712793
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1', '144.bc1', '216.g1', '216.p1', '216.s1'], 'contains': ['864.f1', '864.fe1', '864.fw1', '1296.bc1', '1296.be1', '1296.bf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 325, 1134000, 39957127, 104], 'label': '46656.ir.432.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.x1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712794
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1'], 'contains': ['48.j1', '48.cl1', '48.cm1', '72.p1', '216.cr1', '216.cs1', '216.ct1'], 'core': '96.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684504, 1481684400, 39916800, 6267669018, 325, 269279866800], 'label': '46656.ir.24.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1', 'subgroup_fusion': None, 'weyl_group': '7776.lb'}
  • id: 216712795
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.be1', '216.bb1', '216.bc1', '216.bd1', '216.be1', '216.bf1', '216.bg1', '216.cz1'], 'contains': ['864.e1', '864.cj1', '1296.bk1', '1296.bl1', '1296.bm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 325, 1481684400, 39916800, 1521641624], 'label': '46656.ir.432.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.y1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216712796
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.do1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.h1', '216.bh1', '216.bi1', '216.bj1', '216.bk1', '216.bl1', '216.bm1', '216.da1'], 'contains': ['864.o1', '864.p1', '864.dp1', '1296.b1', '1296.bn1', '1296.bo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 39916800, 269279866800], 'label': '46656.ir.432.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.z1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216712797
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.h1', '144.i1', '216.bn1', '216.bo1', '216.bp1'], 'contains': ['864.g1', '864.s1', '864.dq1', '1296.d1', '1296.bn1', '1296.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 39916800, 435], 'label': '46656.ir.432.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ba1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712798
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.h1', '144.j1', '216.bq1', '216.cu1', '216.db1'], 'contains': ['864.j1', '864.t1', '864.ds1', '1296.c1', '1296.bo1', '1296.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [268280812800, 7, 39916800, 37885034880, 31658054835], 'label': '46656.ir.432.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.br1', 'old_label': '432.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712799
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.i1', '144.j1', '216.br1', '216.bs1', '216.bt1', '216.bu1', '216.bv1', '216.bw1', '216.cv1'], 'contains': ['864.k1', '864.x1', '864.dw1', '1296.e1', '1296.bp1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 7, 325, 39916800, 355419187304], 'label': '46656.ir.432.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bc1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712800
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.k1', '144.m1', '216.bn1', '216.bx1', '216.ce1'], 'contains': ['864.g1', '864.bb1', '864.cu1', '1296.f1', '1296.bq1', '1296.br1', '1296.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 268280812800, 39916800, 6227827200, 104], 'label': '46656.ir.432.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '432.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712801
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.k1', '144.l1', '216.by1'], 'contains': ['864.h1', '864.bc1', '864.cv1', '1296.g1', '1296.bq1', '1296.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 39366316405, 39916800, 6227827200, 382729979624], 'label': '46656.ir.432.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '432.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712802
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ht1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.k1', '144.n1', '216.br1', '216.bz1', '216.ca1'], 'contains': ['864.k1', '864.bf1', '864.da1', '1296.h1', '1296.bq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 325, 39916800, 6227827200, 355419187304], 'label': '46656.ir.432.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bf1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712803
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.l1', '144.m1', '144.n1', '216.bo1', '216.cb1', '216.ce1'], 'contains': ['864.g1', '864.bi1', '864.de1', '1296.i1', '1296.bq1', '1296.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40323593624, 268280812800, 39916800, 40323593520, 6227827200], 'label': '46656.ir.432.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '432.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712804
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.l1', '144.m1', '216.cc1'], 'contains': ['864.l1', '864.bs1', '864.dh1', '1296.k1', '1296.bs1', '1296.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684835, 268280812800, 39916800, 40323593520, 6227827200], 'label': '46656.ir.432.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '432.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712805
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.n1', '12.o1', '12.p1', '12.q1', '12.r1', '12.s1'], 'contains': ['48.e1', '48.h1', '48.k1', '48.r1', '48.bw1', '72.bq1', '72.bs1', '72.bt1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 39916800, 7, 325, 269279866800, 1521641624], 'label': '46656.ir.24.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216712806
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1', '216.bh1', '216.cd1', '216.cf1'], 'contains': ['864.o1', '864.bu1', '864.di1', '1296.j1', '1296.br1', '1296.bt1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800, 269279866800, 6227827200], 'label': '46656.ir.432.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '432.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bi1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712807
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.o1', '144.p1', '216.bs1', '216.ca1', '216.ch1', '216.ci1', '216.cj1', '216.ck1', '216.cz1'], 'contains': ['864.k1', '864.cb1', '864.cj1', '1296.l1', '1296.bu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.432.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bj1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712808
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.o1', '144.q1', '216.bp1', '216.ce1', '216.cm1'], 'contains': ['864.g1', '864.ce1', '864.ck1', '1296.n1', '1296.bu1', '1296.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1521641955, 301891126320, 39957120, 1481684400, 1134000], 'label': '46656.ir.432.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '432.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bk1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712809
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.p1', '144.q1', '216.bq1', '216.cl1', '216.dp1'], 'contains': ['864.j1', '864.cf1', '864.cm1', '1296.m1', '1296.bu1', '1296.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 1481684400, 1134000], 'label': '46656.ir.432.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bn1', 'old_label': '432.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712810
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1', '216.a1', '216.bi1', '216.cf1', '216.cn1', '216.co1', '216.cp1', '216.cq1'], 'contains': ['864.a1', '864.o1', '864.cs1', '1296.o1', '1296.bv1', '1296.bw1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 269279866800, 1134000], 'label': '46656.ir.432.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bm1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712811
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.r1', '144.s1', '144.t1', '216.cl1', '216.cu1', '216.dh1'], 'contains': ['864.j1', '864.dn1', '864.eu1', '1296.p1', '1296.bx1', '1296.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 40320, 39957127], 'label': '46656.ir.432.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712812
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.r1', '144.s1', '216.di1'], 'contains': ['864.n1', '864.do1', '864.ey1', '1296.q1', '1296.bx1', '1296.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 1481684400, 40320, 39957127, 270715783395], 'label': '46656.ir.432.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.di1', 'old_label': '432.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bo1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712813
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1', '216.cn1', '216.da1', '216.dj1'], 'contains': ['864.o1', '864.dp1', '864.ez1', '1296.r1', '1296.bx1', '1296.ca1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800, 269279866800, 39957127], 'label': '46656.ir.432.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '432.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712814
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.r1', '144.u1', '216.cw1'], 'contains': ['864.i1', '864.dr1', '864.fa1', '1296.t1', '1296.by1', '1296.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [293708217925, 355419187304, 40320, 39957127, 37885034880], 'label': '46656.ir.432.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '432.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bq1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216714497
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bz1', '864.ca1', '864.ci1', '1296.hz1'], 'contains': ['5184.r1', '7776.w1', '7776.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [41091120, 387999647280, 463289990028], 'label': '46656.ir.2592.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ex1', 'old_label': '2592.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712815
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.s1', '144.u1', '216.cl1', '216.cx1', '216.db1'], 'contains': ['864.j1', '864.ds1', '864.fb1', '1296.s1', '1296.by1', '1296.bz1', '1296.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [268280812800, 40320, 39957127, 37885034880, 31658054835], 'label': '46656.ir.432.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.br1', 'old_label': '432.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.br1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712816
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.t1', '12.w1'], 'contains': ['48.k1', '48.bj1', '48.ca1', '72.bu1', '72.bv1', '72.bw1', '216.bc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827200, 40320, 1174645], 'label': '46656.ir.24.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1', 'subgroup_fusion': None, 'weyl_group': '576.8389'}
  • id: 216712817
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.t1', '144.u1', '216.ch1', '216.cv1', '216.cy1'], 'contains': ['864.k1', '864.du1', '864.fd1', '1296.u1', '1296.by1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [325, 31658054504, 40320, 39957127, 37885034880], 'label': '46656.ir.432.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bs1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712818
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.v1', '144.w1', '144.x1', '216.bn1', '216.cb1', '216.cm1'], 'contains': ['864.g1', '864.dx1', '864.ge1', '1296.v1', '1296.cb1', '1296.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 39916800, 6227827207, 435], 'label': '46656.ir.432.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712819
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.v1', '144.w1', '216.cc1'], 'contains': ['864.l1', '864.dy1', '864.gl1', '1296.x1', '1296.cb1', '1296.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 1481684835, 268280812800, 39916800, 6227827207], 'label': '46656.ir.432.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '432.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712820
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.w1', '216.bh1', '216.cd1', '216.co1'], 'contains': ['864.o1', '864.dz1', '864.gn1', '1296.w1', '1296.cb1', '1296.cd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.432.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712821
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.w1', '144.y1', '216.bo1', '216.bx1', '216.cm1'], 'contains': ['864.g1', '864.ea1', '864.gu1', '1296.y1', '1296.cc1', '1296.cd1', '1296.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 268280812800, 39916800, 40323593520, 6227827207], 'label': '46656.ir.432.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bw1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712822
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.v1', '144.y1', '216.by1'], 'contains': ['864.h1', '864.eb1', '864.gv1', '1296.z1', '1296.cc1', '1296.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 39916800, 6227827207], 'label': '46656.ir.432.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '432.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bx1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712823
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.x1', '144.y1', '216.br1', '216.bz1', '216.ci1'], 'contains': ['864.k1', '864.ei1', '864.hd1', '1296.ba1', '1296.cc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 325, 39916800, 355419187304, 6227827207], 'label': '46656.ir.432.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.by1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712824
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '144.bb1', '144.bc1', '216.bp1', '216.bx1', '216.cb1'], 'contains': ['864.g1', '864.er1', '864.fk1', '1296.bc1', '1296.cf1', '1296.cg1', '1296.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1481684835, 301891126320, 1481684400, 1134000, 39957127], 'label': '46656.ir.432.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bz1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712825
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '144.ba1', '144.bc1', '216.by1'], 'contains': ['864.h1', '864.es1', '864.fl1', '1296.be1', '1296.cf1', '1296.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [294706903784, 325, 1481684400, 1134000, 39957127], 'label': '46656.ir.432.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '432.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ca1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712826
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '144.ba1', '144.bd1', '216.cw1'], 'contains': ['864.i1', '864.et1', '864.fm1', '1296.bd1', '1296.cf1', '1296.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 325, 1481684400, 1134000, 39957127], 'label': '46656.ir.432.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '432.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cb1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712827
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.u1', '12.w1'], 'contains': ['48.k1', '48.bu1', '48.cb1', '72.bx1', '72.by1', '216.bd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 40320, 1174645], 'label': '46656.ir.24.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216712828
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ba1', '144.bb1', '144.bd1', '216.bq1', '216.cx1', '216.dh1'], 'contains': ['864.j1', '864.eu1', '864.fn1', '1296.bb1', '1296.cf1', '1296.ch1', '1296.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 1134000, 39957127], 'label': '46656.ir.432.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cc1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712829
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bc1', '144.bd1', '216.bs1', '216.bz1', '216.cr1', '216.cy1'], 'contains': ['864.k1', '864.ev1', '864.fu1', '1296.bf1', '1296.cf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [325, 1481684400, 1481684504, 1134000, 39957127], 'label': '46656.ir.432.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cd1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712830
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '144.bb1', '216.cc1'], 'contains': ['864.l1', '864.ew1', '864.fx1', '1296.bi1', '1296.cg1', '1296.ch1', '1296.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [301891126320, 1481684400, 1134000, 39957127, 31658054835], 'label': '46656.ir.432.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '432.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ce1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712831
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '144.ba1'], 'contains': ['864.m1', '864.ex1', '864.fy1', '1296.bj1', '1296.ch1', '1296.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [39366316405, 1481684400, 1134000, 382729979624, 39957127], 'label': '46656.ir.432.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.cf1', 'old_label': '432.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cf1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712832
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cf2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.z1', '144.ba1', '216.cs1'], 'contains': ['864.m2', '864.ex2', '864.fy2', '1296.bj2', '1296.ch1', '1296.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316405, 1481684400, 1134000, 39957127, 387999647384], 'label': '46656.ir.432.cf2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '432.cf2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cf2', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712833
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ba1', '144.bb1', '216.di1'], 'contains': ['864.n1', '864.ey1', '864.fz1', '1296.bg1', '1296.ch1', '1296.ci1', '1296.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 1481684400, 1134000, 39957127, 270715783395], 'label': '46656.ir.432.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.di1', 'old_label': '432.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712834
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bb1', '216.bi1', '216.cd1', '216.ct1', '216.dj1'], 'contains': ['864.o1', '864.ez1', '864.ga1', '1296.bh1', '1296.cg1', '1296.cj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 1134000, 39957127], 'label': '46656.ir.432.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ch1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712835
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.be1', '144.bf1', '216.cw1'], 'contains': ['864.b1', '864.i1', '864.cl1', '1296.bl1', '1296.ck1', '1296.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39957120, 39366316405, 39916800, 31697930984, 37885034880], 'label': '46656.ir.432.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '432.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ci1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712836
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.be1', '144.bg1', '216.cu1', '216.cx1', '216.dp1'], 'contains': ['864.c1', '864.j1', '864.cm1', '1296.bk1', '1296.ck1', '1296.cl1', '1296.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 39916800, 1521641624], 'label': '46656.ir.432.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bn1', 'old_label': '432.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712837
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.be1', '144.bh1', '216.cv1', '216.cy1', '216.cz1'], 'contains': ['864.e1', '864.k1', '864.co1', '1296.bm1', '1296.ck1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 325, 39916800, 31697930984, 37885034880], 'label': '46656.ir.432.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ck1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712838
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.t1', '12.u1'], 'contains': ['48.h1', '48.j1', '48.k1', '48.bv1', '48.by1', '72.br1', '72.bz1', '72.ca1', '72.cb1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 39916800, 41050807, 325, 269279866800, 1521641624], 'label': '46656.ir.24.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712839
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bf1', '144.bg1', '144.bh1', '216.db1', '216.dc1', '216.df1', '216.dh1', '216.dl1', '216.dm1', '216.dp1'], 'contains': ['864.j1', '864.cq1', '1296.ck1', '1296.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [268280812800, 39957120, 31697931315, 39916800, 37885034880], 'label': '46656.ir.432.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '432.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cl1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712840
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bf1', '144.bg1', '216.dd1', '216.di1', '216.dn1'], 'contains': ['864.n1', '864.cr1', '1296.cl1', '1296.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [268280812800, 39957120, 39916800, 37885034880, 1521641624], 'label': '46656.ir.432.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '432.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cm1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712841
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.er1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bg1', '216.a1', '216.da1', '216.de1', '216.dg1', '216.dj1', '216.dk1', '216.do1'], 'contains': ['864.o1', '864.cs1', '1296.cm1', '1296.cn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 39916800, 269279866800], 'label': '46656.ir.432.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cn1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712842
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bi1', '144.bp1', '216.bh1', '216.dq1', '216.dr1', '216.ds1', '216.dt1', '216.du1', '216.dv1'], 'contains': ['864.p1', '864.bu1', '864.dz1', '1296.co1', '1296.cp1', '1296.cq1', '1296.cr1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.432.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.co1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712843
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bi1', '144.bq1', '216.dw1', '216.dx1', '216.dy1'], 'contains': ['864.q1', '864.bx1', '864.el1', '1296.cr1', '1296.cs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [624302466480, 7, 270715782960, 40323593520, 6227827207], 'label': '46656.ir.432.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '432.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cp1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712844
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bj1', '144.br1', '216.dw1', '216.dz1', '216.ea1'], 'contains': ['864.q1', '864.ch1', '864.fi1', '1296.ct1', '1296.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 655477406640, 269279866800], 'label': '46656.ir.432.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '432.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cq1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712845
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bj1', '144.bs1', '216.bi1', '216.dq1', '216.eb1', '216.ec1', '216.ed1'], 'contains': ['864.a1', '864.p1', '864.ga1', '1296.cu1', '1296.cv1', '1296.cw1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 1481684400, 269279866800], 'label': '46656.ir.432.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cr1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712846
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bt1', '216.bi1', '216.da1', '216.dv1', '216.ee1', '216.ef1', '216.eg1', '216.eh1', '216.ei1', '216.ej1', '216.ek1', '216.el1', '216.em1', '216.en1', '216.eo1', '216.ep1'], 'contains': ['864.p1', '864.cs1', '864.ez1', '1296.cx1', '1296.cy1', '1296.cz1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 269279866800], 'label': '46656.ir.432.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cs1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712847
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bk1', '144.bu1', '216.bh1', '216.dq1', '216.ee1', '216.eq1', '216.er1', '216.es1', '216.et1'], 'contains': ['864.p1', '864.di1', '864.gn1', '1296.da1', '1296.db1', '1296.dc1', '1296.dd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1481684400, 269279866800], 'label': '46656.ir.432.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ct1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712848
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bk1', '144.bv1', '216.dw1', '216.eu1', '216.ev1'], 'contains': ['864.q1', '864.dj1', '864.gp1', '1296.dc1', '1296.de1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 655477406640, 269279866800], 'label': '46656.ir.432.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '432.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cu1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712849
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '12.u1', '12.ba1'], 'contains': ['48.k1', '48.bx1', '48.cc1', '72.cc1', '72.cd1', '216.bf1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 269279866800, 40320], 'label': '46656.ir.24.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216712850
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bk1', '144.bw1', '216.ew1'], 'contains': ['864.r1', '864.dk1', '864.gr1', '1296.dc1', '1296.df1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 269279866800, 623823424560], 'label': '46656.ir.432.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '432.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cv1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216712851
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '144.bl1', '216.bj1', '216.dr1', '216.eb1', '216.ef1', '216.eq1'], 'contains': ['864.p1', '1296.dg1', '1296.do1', '1296.dw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 499, 1481684400, 269279866800, 1481684844], 'label': '46656.ir.432.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cw1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216712852
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.do1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1', '216.bj1', '216.bk1', '216.ds1', '216.ec1', '216.eh1', '216.ei1', '216.er1'], 'contains': ['864.p1', '1296.dh1', '1296.dp1', '1296.dq1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39366316080, 1481684400, 269279866800, 1481684844], 'label': '46656.ir.432.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cx1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216712853
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1', '144.bm1', '216.bl1', '216.dr1', '216.dt1', '216.ed1', '216.ek1', '216.er1', '216.es1'], 'contains': ['864.p1', '1296.di1', '1296.dj1', '1296.dr1', '1296.dx1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 39366316080, 1481684400, 6227827818, 269279866800], 'label': '46656.ir.432.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712854
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '144.bn1', '216.bm1', '216.du1', '216.eb1', '216.eh1', '216.es1'], 'contains': ['864.p1', '1296.dk1', '1296.ds1', '1296.dy1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091619, 39366316080, 1481684400, 269279866800, 1481684844], 'label': '46656.ir.432.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cz1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712855
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1', '216.bk1', '216.bm1', '216.dt1', '216.ec1', '216.ef1', '216.el1', '216.et1'], 'contains': ['864.p1', '1296.dl1', '1296.dt1', '1296.du1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 39957619, 1481684844], 'label': '46656.ir.432.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.da1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712856
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1', '144.bo1', '216.bl1', '216.ds1', '216.du1', '216.ed1', '216.em1', '216.eq1', '216.et1'], 'contains': ['864.p1', '1296.dm1', '1296.dn1', '1296.dv1', '1296.dz1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 39366316080, 6267744618, 1481684400, 269279866800], 'label': '46656.ir.432.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.db1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712857
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1', '144.bl1', '216.dx1', '216.dz1', '216.eu1'], 'contains': ['864.q1', '1296.dw1', '1296.ea1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 499, 655477406640, 444, 269279866800], 'label': '46656.ir.432.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '432.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dc1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712858
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1', '144.bm1', '216.dx1', '216.ea1', '216.ev1'], 'contains': ['864.q1', '1296.dx1', '1296.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [469, 624302466480, 270715782960, 6227827818, 40323593520], 'label': '46656.ir.432.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '432.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dd1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712859
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1', '144.bn1', '216.dy1', '216.dz1', '216.ev1'], 'contains': ['864.q1', '1296.dy1', '1296.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091619, 39366316080, 655477406640, 444, 269279866800], 'label': '46656.ir.432.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '432.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.de1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712860
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '12.t1', '12.ba1'], 'contains': ['48.k1', '48.bz1', '48.cd1', '72.ce1', '72.cf1', '72.cg1', '216.bg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 269279866800, 40320, 1174645], 'label': '46656.ir.24.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216712861
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1', '144.bo1', '216.dy1', '216.ea1', '216.eu1'], 'contains': ['864.q1', '1296.dz1', '1296.ed1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [469, 39366316080, 6267744618, 655477406640, 269279866800], 'label': '46656.ir.432.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '432.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.df1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712862
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1', '144.bl1', '216.ew1'], 'contains': ['864.r1', '1296.dw1', '1296.ee1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 499, 444, 269279866800, 623823424560], 'label': '46656.ir.432.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cq1', 'old_label': '432.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dg1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216712863
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1', '144.bo1', '216.ew1'], 'contains': ['864.r1', '1296.dz1', '1296.ef1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [469, 39366316080, 6267744618, 269279866800, 623823424560], 'label': '46656.ir.432.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '432.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dh1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216712864
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bp1', '144.bx1', '216.bn1', '216.ex1', '216.fc1'], 'contains': ['864.s1', '864.bb1', '864.dx1', '1296.co1', '1296.eg1', '1296.eh1', '1296.ei1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 6227827207, 104], 'label': '46656.ir.432.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712865
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bp1', '144.by1', '216.bo1', '216.ez1', '216.fc1'], 'contains': ['864.s1', '864.bi1', '864.ea1', '1296.cp1', '1296.eg1', '1296.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [268280812800, 7, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.432.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dj1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712866
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bp1', '144.bz1', '216.b1', '216.fa1', '216.fd1'], 'contains': ['864.t1', '864.bj1', '864.ec1', '1296.cq1', '1296.ei1', '1296.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.432.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dk1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712867
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bp1', '144.bq1', '144.ca1', '216.fb1'], 'contains': ['864.u1', '864.bk1', '864.ed1', '1296.cr1', '1296.eh1', '1296.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593624, 7, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.432.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cs1', 'old_label': '432.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712868
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bq1', '144.cb1', '216.ey1'], 'contains': ['864.v1', '864.bl1', '864.ef1', '1296.cs1', '1296.eh1', '1296.ek1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387999647280, 7, 93536397441, 6227827207, 387999647384], 'label': '46656.ir.432.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '432.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712869
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.br1', '144.cc1', '216.ey1'], 'contains': ['864.v1', '864.bz1', '864.ff1', '1296.ct1', '1296.el1', '1296.en1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 387999647280, 7, 93536397441, 387999647384], 'label': '46656.ir.432.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '432.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712870
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bs1', '144.cd1', '216.bp1', '216.ex1', '216.ez1'], 'contains': ['864.s1', '864.ce1', '864.fk1', '1296.cu1', '1296.em1', '1296.en1', '1296.eo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 7, 269279866800, 37885034880, 31658054835], 'label': '46656.ir.432.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.do1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712871
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.v1', '12.x1', '12.y1'], 'contains': ['48.ce1', '72.a1', '72.ci1', '72.cj1', '96.m1', '648.cv1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [624190336641, 39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 1521641624], 'label': '46656.ir.24.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216712872
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bs1', '144.ce1', '216.c1', '216.bq1', '216.fa1'], 'contains': ['864.t1', '864.cf1', '864.fn1', '1296.cv1', '1296.em1', '1296.eo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 31658054504, 37885034880], 'label': '46656.ir.432.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712873
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.br1', '144.bs1', '144.cf1', '216.fb1'], 'contains': ['864.u1', '864.cg1', '864.fo1', '1296.cw1', '1296.en1', '1296.eo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 269279866800, 435], 'label': '46656.ir.432.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '432.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dq1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216712874
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bt1', '144.cg1', '216.bp1', '216.fc1', '216.fe1'], 'contains': ['864.s1', '864.ck1', '864.er1', '1296.cx1', '1296.ep1', '1296.er1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1521641955, 301891126320, 39957120, 7, 1481684400], 'label': '46656.ir.432.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dr1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712875
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bt1', '144.ch1', '216.bq1', '216.cu1', '216.fi1'], 'contains': ['864.t1', '864.cm1', '864.eu1', '1296.cy1', '1296.ep1', '1296.eq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 7, 1481684400], 'label': '46656.ir.432.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ds1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712876
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bt1', '144.ci1', '216.c1', '216.db1', '216.fd1', '216.ff1', '216.fg1', '216.fh1', '216.fi1'], 'contains': ['864.t1', '864.cq1', '864.fb1', '1296.cz1', '1296.eq1', '1296.er1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 31697931315, 37885034880], 'label': '46656.ir.432.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '432.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dt1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216712877
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bu1', '144.cj1', '216.bn1', '216.ez1', '216.fe1'], 'contains': ['864.s1', '864.cu1', '864.ge1', '1296.da1', '1296.es1', '1296.et1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 435], 'label': '46656.ir.432.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.du1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712878
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bu1', '144.ck1', '216.b1', '216.fa1', '216.ff1'], 'contains': ['864.t1', '864.cw1', '864.gf1', '1296.db1', '1296.es1', '1296.ev1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684835, 7, 1481684400], 'label': '46656.ir.432.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712879
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bu1', '144.bv1', '144.bw1', '144.cl1', '216.fb1'], 'contains': ['864.u1', '864.cx1', '864.gg1', '1296.dc1', '1296.es1', '1296.eu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 269279866800, 104], 'label': '46656.ir.432.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '432.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712880
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bu1', '144.cm1', '216.bo1', '216.ex1', '216.fe1'], 'contains': ['864.s1', '864.de1', '864.gu1', '1296.dd1', '1296.et1', '1296.eu1', '1296.ev1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 7, 40323593520], 'label': '46656.ir.432.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dx1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712881
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bv1', '144.cn1', '216.ey1'], 'contains': ['864.v1', '864.df1', '864.gx1', '1296.de1', '1296.eu1', '1296.ew1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 555805963521, 7, 294706903784, 388956924720], 'label': '46656.ir.432.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '432.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dy1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216712882
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['11664.b1', '11664.bj1', '11664.bk1', '11664.r1', '11664.u1', '11664.x1', '11664.e1', '11664.s1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.g1'], 'contains': ['8.b1', '12.by1', '16.f1', '36.cb1', '108.ez1'], 'core': '4.h1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 7, 41051125, 6227827818, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': ['2.c1', '2.d1', '2.g1'], 'normal_contains': ['8.b1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '46656.ir', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712883
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.z1'], 'contains': ['48.cf1', '72.ci1', '72.cj1', '96.n1', '648.cw1'], 'core': '216.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [39366316080, 461333739315, 39957120, 41050800, 1481684400, 39916800, 269279866800, 1521641624], 'label': '46656.ir.24.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '24.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216712884
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.bw1', '144.co1'], 'contains': ['864.w1', '864.dg1', '864.gz1', '1296.df1', '1296.eu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 7, 325, 130941987578, 388956924720], 'label': '46656.ir.432.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bw1', 'old_label': '432.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dz1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 216712885
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bx1', '144.by1', '216.br1', '216.fj1', '216.fm1', '216.fn1', '216.fo1', '216.fp1', '216.fw1'], 'contains': ['864.x1', '864.bf1', '864.ei1', '1296.eg1', '1296.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.432.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ea1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712886
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bx1', '144.ca1', '144.cb1', '216.fk1', '216.fq1', '216.fr1'], 'contains': ['864.y1', '864.bg1', '864.ej1', '1296.eh1', '1296.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [387999647280, 7, 325, 6227827207, 387999647384], 'label': '46656.ir.432.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cf1', 'old_label': '432.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eb1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712887
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bx1', '144.bz1', '216.d1', '216.fl1', '216.fs1', '216.ft1', '216.fu1', '216.fv1', '216.gf1'], 'contains': ['864.z1', '864.bh1', '864.ek1', '1296.ei1', '1296.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 7, 325, 6227827207, 104], 'label': '46656.ir.432.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ec1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712888
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.by1', '144.bz1', '144.ca1', '216.e1', '216.fy1', '216.fz1', '216.ga1', '216.gb1', '216.gc1', '216.gf1'], 'contains': ['864.z1', '864.bq1', '864.ep1', '1296.ej1', '1296.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.432.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '432.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ed1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712889
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.eh1', '144.cb1', '216.fx1', '216.gd1', '216.ge1'], 'contains': ['864.ba1', '864.br1', '864.eq1', '1296.ek1', '1296.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6227827207, 7, 104, 325, 461482882830], 'label': '46656.ir.432.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '432.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ee1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712890
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bh1', '144.cc1', '216.fx1', '216.gg1', '216.gh1'], 'contains': ['864.ba1', '864.by1', '864.fh1', '1296.el1', '1296.ey1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 7, 325, 174452060430, 104], 'label': '46656.ir.432.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ef1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712891
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cd1', '144.ce1', '216.f1', '216.bs1', '216.fj1', '216.gi1', '216.gj1', '216.gk1', '216.gl1'], 'contains': ['864.x1', '864.cb1', '864.fu1', '1296.em1', '1296.ey1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.432.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eg1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712892
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cc1', '144.cd1', '144.cf1', '216.fk1', '216.gm1', '216.gn1'], 'contains': ['864.y1', '864.cc1', '864.fv1', '1296.en1', '1296.ey1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 301891126320, 7, 325, 104], 'label': '46656.ir.432.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '432.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eh1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712893
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cd1', '144.ce1', '144.cf1', '216.g1', '216.fl1', '216.fy1', '216.go1', '216.gp1', '216.gq1', '216.gr1'], 'contains': ['864.z1', '864.cd1', '864.fw1', '1296.eo1', '1296.ey1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 104], 'label': '46656.ir.432.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ei1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712894
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.j1', '8.h1'], 'contains': ['48.l1', '48.m1', '48.n1', '48.bl1', '48.bm1', '48.br1', '48.ck1', '72.ck1', '72.cs1', '72.cu1'], 'core': '864.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [41091120, 39366316080, 622713415418, 7, 325, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.24.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '24.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216712895
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cg1', '144.ch1', '216.bb1', '216.bs1', '216.fw1', '216.gs1', '216.gt1', '216.gu1', '216.gv1', '216.gw1', '216.gx1', '216.gy1', '216.gz1', '216.ha1', '216.hb1', '216.hc1', '216.hn1'], 'contains': ['864.x1', '864.cj1', '864.ev1', '1296.ep1', '1296.ez1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 7, 325, 1481684400, 1521641624], 'label': '46656.ir.432.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ej1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712896
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ch1', '144.ci1', '216.f1', '216.cv1', '216.he1', '216.hf1', '216.hg1', '216.hh1', '216.hn1'], 'contains': ['864.x1', '864.co1', '864.fd1', '1296.eq1', '1296.ez1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 7, 325, 31697930984, 37885034880], 'label': '46656.ir.432.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ek1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712897
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cg1', '144.ci1', '216.g1', '216.gf1', '216.hd1', '216.hi1', '216.hj1', '216.hk1', '216.hl1'], 'contains': ['864.z1', '864.cp1', '864.fe1', '1296.er1', '1296.ez1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [387037284480, 39957120, 7, 325, 39957224], 'label': '46656.ir.432.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.el1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712898
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cj1', '144.ck1', '144.cl1', '216.d1', '216.fy1', '216.hd1', '216.ho1', '216.hp1', '216.hq1', '216.hr1'], 'contains': ['864.z1', '864.ct1', '864.gk1', '1296.es1', '1296.fa1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 104], 'label': '46656.ir.432.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.em1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712899
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cj1', '144.cm1', '216.br1', '216.fj1', '216.gs1', '216.hs1', '216.ht1', '216.hu1', '216.hv1'], 'contains': ['864.x1', '864.da1', '864.hd1', '1296.et1', '1296.fa1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 325, 355419187304], 'label': '46656.ir.432.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.en1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712900
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cl1', '144.cm1', '144.cn1', '144.co1', '216.fk1', '216.hw1', '216.hx1'], 'contains': ['864.y1', '864.db1', '864.he1', '1296.eu1', '1296.fa1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 301891126320, 7, 325, 104], 'label': '46656.ir.432.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '432.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eo1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712901
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ck1', '144.cm1', '216.e1', '216.fl1', '216.hd1', '216.hy1', '216.hz1', '216.ia1', '216.ib1'], 'contains': ['864.z1', '864.dc1', '864.hf1', '1296.ev1', '1296.fa1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744007, 7, 325, 40323593520], 'label': '46656.ir.432.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ep1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712902
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ew1', '144.cn1', '216.fx1', '216.ic1', '216.id1'], 'contains': ['864.ba1', '864.dd1', '864.hg1', '1296.ew1', '1296.fa1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 7, 325, 174451657230, 104], 'label': '46656.ir.432.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eq1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712903
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.de1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cp1', '144.cx1', '216.h1', '216.bt1', '216.fm1', '216.gi1', '216.gt1', '216.he1', '216.hs1'], 'contains': ['864.x1', '1296.a1', '3888.by1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [499, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.432.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.er1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712904
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cy1', '144.cz1', '216.h1', '216.i1', '216.bu1', '216.gj1', '216.gv1', '216.hf1', '216.hg1'], 'contains': ['864.x1', '1296.fb1', '3888.bz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39917299, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.432.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.es1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712905
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '12.v1', '12.bb1', '12.bc1'], 'contains': ['48.ce1', '72.cp1', '72.cy1', '96.e1', '648.gx1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 622713012218, 7, 41051125, 269279866800], 'label': '46656.ir.24.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216712906
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cq1', '144.cz1', '216.j1', '216.bt1', '216.fn1', '216.gk1', '216.gw1', '216.hg1', '216.ht1'], 'contains': ['864.x1', '1296.fb1', '3888.ca1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39917299, 268280812800, 7, 325, 355419187304], 'label': '46656.ir.432.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.et1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712907
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cr1', '144.cs1', '216.bv1', '216.fm1', '216.fo1', '216.gl1', '216.gy1', '216.ht1', '216.hu1'], 'contains': ['864.x1', '1296.fc1', '3888.cb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 7, 325, 6227827818, 355419187304], 'label': '46656.ir.432.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.eu1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712908
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ct1', '144.db1', '216.k1', '216.bw1', '216.fp1', '216.gi1', '216.gw1', '216.hf1', '216.hu1'], 'contains': ['864.x1', '1296.fd1', '3888.cc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091619, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.432.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ev1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712909
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cu1', '144.dc1', '216.i1', '216.bw1', '216.fo1', '216.gk1', '216.gt1', '216.hh1', '216.hv1'], 'contains': ['864.x1', '1296.fe1', '3888.cd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 325, 1481684400, 1481684504, 39957619], 'label': '46656.ir.432.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ew1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712910
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dc1', '144.dd1', '216.j1', '216.k1', '216.bu1', '216.gj1', '216.gz1', '216.he1', '216.hh1'], 'contains': ['864.x1', '1296.fe1', '3888.ce1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7, 325, 31658054504, 39957619, 37885034880], 'label': '46656.ir.432.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ex1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712911
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cv1', '144.cw1', '216.bv1', '216.fn1', '216.fp1', '216.gl1', '216.ha1', '216.hs1', '216.hv1'], 'contains': ['864.x1', '1296.ff1', '3888.cf1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 6267744618, 7, 325, 355419187304], 'label': '46656.ir.432.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ey1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712912
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cp1', '144.df1', '144.dj1', '144.dn1', '216.fq1', '216.gm1', '216.hw1'], 'contains': ['864.y1', '1296.a1', '3888.cg1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [301891126320, 499, 7, 325, 104], 'label': '46656.ir.432.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '432.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ez1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712913
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cr1', '144.dg1', '144.dk1', '216.fq1', '216.gn1', '216.hx1'], 'contains': ['864.y1', '1296.fc1', '3888.ch1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [387999647280, 7, 325, 6227827818, 387999647384], 'label': '46656.ir.432.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cf1', 'old_label': '432.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fa1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712914
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ct1', '144.dh1', '144.dl1', '216.fr1', '216.gm1', '216.hx1'], 'contains': ['864.y1', '1296.fd1', '3888.ci1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091619, 301891126320, 7, 325, 104], 'label': '46656.ir.432.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '432.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fb1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712915
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cw1', '144.di1', '144.dm1', '144.do1', '216.fr1', '216.gn1', '216.hw1'], 'contains': ['864.y1', '1296.ff1', '3888.cj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [301891126320, 6267744618, 7, 325, 104], 'label': '46656.ir.432.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '432.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fc1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712916
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '12.f1', '12.bd1', '12.be1'], 'contains': ['48.a1', '48.o1', '48.s1', '48.bf1', '48.bi1', '48.bt1', '48.ch1', '72.cs1', '72.cz1', '72.df1', '72.dg1', '72.dh1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.24.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216712917
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cp1', '144.cx1', '144.df1', '216.l1', '216.fs1', '216.fz1', '216.go1', '216.hi1', '216.ho1', '216.hy1'], 'contains': ['864.z1', '1296.a1', '3888.ck1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 499, 7, 325, 104], 'label': '46656.ir.432.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '432.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fd1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712918
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cq1', '144.cy1', '216.l1', '216.ft1', '216.ga1', '216.gp1', '216.hj1', '216.hp1', '216.hz1'], 'contains': ['864.z1', '1296.fb1', '3888.cl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39917299, 39366316080, 7, 325, 104], 'label': '46656.ir.432.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fe1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712919
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cr1', '144.da1', '216.m1', '216.fs1', '216.gb1', '216.gq1', '216.hk1', '216.hp1', '216.ia1'], 'contains': ['864.z1', '1296.fc1', '3888.cm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 7, 325, 6227827818, 104], 'label': '46656.ir.432.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ff1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712920
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cs1', '144.da1', '144.dg1', '216.n1', '216.fu1', '216.fz1', '216.gr1', '216.hk1', '216.hq1', '216.hz1'], 'contains': ['864.z1', '1296.fc1', '3888.cn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 7, 325, 6227827818, 40323593520], 'label': '46656.ir.432.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '432.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fg1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712921
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ct1', '144.db1', '144.dh1', '216.o1', '216.fv1', '216.gc1', '216.go1', '216.hj1', '216.hq1', '216.ia1'], 'contains': ['864.z1', '1296.fd1', '3888.co1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091619, 39366316080, 7, 325, 104], 'label': '46656.ir.432.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fh1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712922
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cu1', '144.dd1', '216.o1', '216.fu1', '216.gb1', '216.gp1', '216.hi1', '216.hr1', '216.ib1'], 'contains': ['864.z1', '1296.fe1', '3888.cp1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [387037284480, 7, 325, 39957619, 104], 'label': '46656.ir.432.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fi1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712923
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cv1', '144.de1', '144.di1', '216.m1', '216.ft1', '216.gc1', '216.gr1', '216.hl1', '216.ho1', '216.ib1'], 'contains': ['864.z1', '1296.ff1', '3888.cq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 6267744618, 7, 325, 104], 'label': '46656.ir.432.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fj1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712924
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cw1', '144.de1', '216.n1', '216.fv1', '216.ga1', '216.gq1', '216.hl1', '216.hr1', '216.hy1'], 'contains': ['864.z1', '1296.ff1', '3888.cr1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744618, 7, 325, 40323593520], 'label': '46656.ir.432.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fk1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712925
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ca1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ex1', '144.dj1', '216.gd1', '216.gg1', '216.ic1'], 'contains': ['864.ba1', '1296.a1', '3888.cs1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [499, 7, 104, 325, 461482882830], 'label': '46656.ir.432.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '432.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fl1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712926
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ez1', '144.dk1', '216.gd1', '216.gh1', '216.id1'], 'contains': ['864.ba1', '1296.fc1', '3888.ct1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7, 325, 6227827818, 104, 461482882830], 'label': '46656.ir.432.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '432.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fm1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712927
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1', '12.d1', '12.bd1', '12.bf1'], 'contains': ['48.b1', '48.o1', '48.w1', '72.da1', '72.di1', '72.dm1', '72.dq1', '216.dr1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6227827207, 499, 7, 325, 269279866800], 'label': '46656.ir.24.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216712928
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ey1', '144.dl1', '216.ge1', '216.gg1', '216.id1'], 'contains': ['864.ba1', '1296.fd1', '3888.cu1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091619, 7, 325, 174452060430, 104], 'label': '46656.ir.432.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fn1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712929
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fa1', '144.dm1', '216.ge1', '216.gh1', '216.ic1'], 'contains': ['864.ba1', '1296.ff1', '3888.cv1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744618, 7, 104, 325, 174451657230], 'label': '46656.ir.432.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fo1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712930
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dp1', '144.du1', '216.ca1', '216.fj1', '216.if1'], 'contains': ['864.bf1', '864.cb1', '864.da1', '1296.fg1', '1296.fh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 268280812800, 325, 6227827200, 355419187304], 'label': '46656.ir.432.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '432.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fp1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712931
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dp1', '144.dt1', '144.dw1', '216.fk1'], 'contains': ['864.bg1', '864.cc1', '864.db1', '1296.fg1', '1296.fi1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 387999647280, 325, 6227827200, 387999647384], 'label': '46656.ir.432.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fq1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712932
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dp1', '144.dv1', '216.t1', '216.fl1', '216.ie1'], 'contains': ['864.bh1', '864.cd1', '864.dc1', '1296.fg1', '1296.fj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 6227827200, 104], 'label': '46656.ir.432.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fr1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712933
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dp1', '144.dx1', '216.ce1', '216.ex1', '216.ig1'], 'contains': ['864.bb1', '864.ce1', '864.de1', '1296.fh1', '1296.fi1', '1296.fj1', '1296.fk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 6227827200, 104], 'label': '46656.ir.432.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '432.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712934
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dq1', '144.dz1', '216.bn1', '216.ig1', '216.ip1'], 'contains': ['864.bb1', '864.dq1', '864.ge1', '1296.fl1', '1296.fm1', '1296.fn1', '1296.fo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 6227827200, 435], 'label': '46656.ir.432.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ft1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712935
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dq1', '144.dy1', '216.iq1'], 'contains': ['864.be1', '864.dt1', '864.gh1', '1296.fl1', '1296.fn1', '1296.fp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 268280812904, 6227827200], 'label': '46656.ir.432.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '432.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fu1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216712936
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dq1', '144.ea1', '216.d1', '216.ie1', '216.ir1'], 'contains': ['864.bh1', '864.dv1', '864.gk1', '1296.fl1', '1296.fq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 6227827200, 104], 'label': '46656.ir.432.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fv1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712937
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dq1', '144.eb1', '216.br1', '216.if1', '216.ii1'], 'contains': ['864.bf1', '864.dw1', '864.hd1', '1296.fo1', '1296.fp1', '1296.fq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 268280812800, 325, 6227827200, 355419187304], 'label': '46656.ir.432.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712938
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.be1', '12.bg1'], 'contains': ['48.o1', '48.v1', '48.y1', '72.db1', '72.dj1', '72.dn1', '216.ds1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39917299, 39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.24.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216712939
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dr1', '144.ed1', '216.bx1', '216.fc1', '216.ig1'], 'contains': ['864.bb1', '864.ea1', '864.er1', '1296.fr1', '1296.fs1', '1296.ft1', '1296.fu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40323593624, 1174327, 268280812800, 40323593520, 6227827207], 'label': '46656.ir.432.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712940
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dr1', '144.ec1', '216.by1'], 'contains': ['864.bc1', '864.eb1', '864.es1', '1296.fr1', '1296.ft1', '1296.fv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1174327, 268280812800, 294706903784, 301891126645, 6227827207], 'label': '46656.ir.432.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '432.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fy1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216712941
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dr1', '144.ee1', '216.bz1', '216.fw1', '216.if1'], 'contains': ['864.bf1', '864.ei1', '864.ev1', '1296.fr1', '1296.fw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 268280812800, 325, 355419187304, 6227827207], 'label': '46656.ir.432.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '432.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.fz1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216712942
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dr1', '144.ef1', '216.p1', '216.gf1', '216.ie1'], 'contains': ['864.bh1', '864.ep1', '864.fe1', '1296.fu1', '1296.fv1', '1296.fw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 1174327, 325, 40323593520, 6227827207], 'label': '46656.ir.432.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ga1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712943
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ds1', '144.ej1', '216.bx1', '216.ex1', '216.ip1'], 'contains': ['864.bb1', '864.fk1', '864.gu1', '1296.fx1', '1296.fy1', '1296.fz1', '1296.ge1', '1296.gf1', '1296.gg1', '1296.gh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827200, 41091127, 435], 'label': '46656.ir.432.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gb1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712944
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ds1', '144.eh1', '216.by1'], 'contains': ['864.bc1', '864.fl1', '864.gv1', '1296.fx1', '1296.gb1', '1296.gc1', '1296.gf1', '1296.gi1', '1296.gi2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [268280812800, 39366316405, 6227827200, 382729979624, 41091127], 'label': '46656.ir.432.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '432.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gc1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712945
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ds1', '144.ek1'], 'contains': ['864.bd1', '864.fp1', '864.gw1', '1296.fy1', '1296.ga1', '1296.gb1', '1296.gc1', '1296.gg1', '1296.gi1', '1296.gi2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [387999647280, 39366316405, 6227827200, 355419187304, 41091127], 'label': '46656.ir.432.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.gd1', 'old_label': '432.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gd1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 216712946
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ds1', '144.ei1', '216.iq1'], 'contains': ['864.be1', '864.fr1', '864.hb1', '1296.fz1', '1296.ga1', '1296.gb1', '1296.gh1', '1296.gi1', '1296.gi2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 268280813125, 6227827200, 355419187304, 41091127], 'label': '46656.ir.432.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '432.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ge1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712947
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ds1', '144.el1', '216.bz1', '216.fj1', '216.ii1'], 'contains': ['864.bf1', '864.fu1', '864.hd1', '1296.fx1', '1296.ga1', '1296.gd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 325, 6227827200, 355419187304, 41091127], 'label': '46656.ir.432.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '432.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gf1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712948
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ds1', '144.eg1', '144.en1', '216.fk1'], 'contains': ['864.bg1', '864.fv1', '864.he1', '1296.fy1', '1296.gb1', '1296.gd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [387999647280, 325, 6227827200, 387999647384, 41091127], 'label': '46656.ir.432.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gg1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712949
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.be1', '12.bf1'], 'contains': ['48.o1', '48.w1', '48.x1', '72.dc1', '72.dk1', '72.do1', '216.dt1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1174819, 1481684400, 6227827207, 7, 325, 269279866800], 'label': '46656.ir.24.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216712950
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ds1', '144.em1', '216.p1', '216.fl1', '216.ir1'], 'contains': ['864.bh1', '864.fw1', '864.hf1', '1296.fz1', '1296.gc1', '1296.gd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 325, 6227827200, 104, 41091127], 'label': '46656.ir.432.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gh1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712991
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eo1', '144.ep1', '216.iq1'], 'contains': ['864.be1', '864.bm1', '864.cn1', '1296.gk1', '1296.hk1', '1296.hm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268281987445, 39366316080, 1174320, 6227827200, 355419187304], 'label': '46656.ir.432.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '432.hs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216712951
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.gi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eo1', '216.bc1', '216.ca1', '216.fw1', '216.ih1', '216.ii1', '216.ij1', '216.ik1'], 'contains': ['864.bf1', '864.cj1', '1296.gj1', '1296.gk1', '1296.gl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 6227827200, 355419187304, 1174645], 'label': '46656.ir.432.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gi1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216712952
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bo1', '144.dt1', '216.fx1'], 'contains': ['864.br1', '864.by1', '864.dd1', '1296.fg1', '1296.gm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 325, 174452060430, 6227827200, 104], 'label': '46656.ir.432.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gj1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712953
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.du1', '144.dv1', '144.dw1', '216.t1', '216.fy1', '216.il1'], 'contains': ['864.bq1', '864.cd1', '864.ct1', '1296.fg1', '1296.gn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091120, 325, 40323593520, 6227827200], 'label': '46656.ir.432.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gk1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712954
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dt1', '144.es1', '216.ey1'], 'contains': ['864.bl1', '864.bz1', '864.df1', '1296.fi1', '1296.gm1', '1296.go1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [41091120, 387999647280, 93536397441, 6227827200, 387999647384], 'label': '46656.ir.432.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.de1', 'old_label': '432.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712955
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.du1', '144.dx1', '216.ce1', '216.ez1', '216.in1'], 'contains': ['864.bi1', '864.ce1', '864.cu1', '1296.fh1', '1296.gn1', '1296.gp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41091120, 268280812800, 40323593955, 40323593520, 6227827200], 'label': '46656.ir.432.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '432.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712956
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dv1', '144.dx1', '216.u1', '216.fa1', '216.im1'], 'contains': ['864.bj1', '864.cf1', '864.cw1', '1296.fj1', '1296.gn1', '1296.gq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684835, 1481684400, 6227827200], 'label': '46656.ir.432.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '432.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712957
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dw1', '144.dx1', '144.es1', '216.fb1'], 'contains': ['864.bk1', '864.cg1', '864.cx1', '1296.fi1', '1296.gn1', '1296.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [41091120, 40323593955, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.432.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.dh1', 'old_label': '432.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.go1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712958
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dx1', '144.et1', '216.cf1', '216.dq1', '216.io1'], 'contains': ['864.a1', '864.bu1', '864.di1', '1296.fk1', '1296.gp1', '1296.gq1', '1296.gr1'], 'core': '864.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.432.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '432.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gp1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712959
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dy1', '144.dz1', '144.ea1', '216.b1', '216.im1', '216.it1'], 'contains': ['864.bj1', '864.dn1', '864.gf1', '1296.fl1', '1296.gs1', '1296.gt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684835, 1481684400, 6227827200], 'label': '46656.ir.432.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712960
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1', '12.e1', '12.bd1', '12.bg1'], 'contains': ['48.c1', '48.o1', '48.y1', '72.dd1', '72.dl1', '72.dp1', '72.dr1', '216.du1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6227827207, 7, 41091619, 325, 269279866800], 'label': '46656.ir.24.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216712961
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dy1', '144.dz1', '216.iu1'], 'contains': ['864.bt1', '864.do1', '864.gm1', '1296.fn1', '1296.gs1', '1296.gv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 6227827200, 270715783395], 'label': '46656.ir.432.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iu1', 'old_label': '432.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gr1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712962
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dz1', '216.bh1', '216.io1', '216.iv1'], 'contains': ['864.bu1', '864.dp1', '864.gn1', '1296.fm1', '1296.gs1', '1296.gu1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.432.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gs1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712963
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dz1', '144.eb1', '216.bo1', '216.in1', '216.ip1'], 'contains': ['864.bi1', '864.dq1', '864.gu1', '1296.fo1', '1296.gt1', '1296.gu1', '1296.gv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 268280812800, 40323593955, 40323593520, 6227827200], 'label': '46656.ir.432.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gt1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712964
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.dy1', '144.eb1', '216.iq1'], 'contains': ['864.bm1', '864.dt1', '864.hb1', '1296.fp1', '1296.gt1', '1296.gv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39916807, 301891126645, 40323593520, 6227827200, 355419187304], 'label': '46656.ir.432.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fz1', 'old_label': '432.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gu1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712965
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ea1', '144.eb1', '216.e1', '216.il1', '216.ir1'], 'contains': ['864.bq1', '864.dv1', '864.hf1', '1296.fq1', '1296.gt1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 39916807, 325, 40323593520, 6227827200], 'label': '46656.ir.432.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712966
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ec1', '144.ed1', '144.ee1', '216.cb1', '216.fc1', '216.in1'], 'contains': ['864.bi1', '864.dx1', '864.er1', '1296.fr1', '1296.gw1', '1296.gx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1174327, 39366316080, 268280812800, 6227827207, 435], 'label': '46656.ir.432.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712967
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ec1', '144.ed1', '216.cc1'], 'contains': ['864.bs1', '864.dy1', '864.ew1', '1296.ft1', '1296.gw1', '1296.gz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684835, 268280812800, 6227827207], 'label': '46656.ir.432.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '432.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712968
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ed1', '216.cd1', '216.dv1', '216.io1'], 'contains': ['864.bu1', '864.dz1', '864.ez1', '1296.fs1', '1296.gw1', '1296.gy1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.432.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216712969
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ed1', '144.ef1', '216.q1', '216.fd1', '216.im1'], 'contains': ['864.bj1', '864.ec1', '864.fb1', '1296.fu1', '1296.gx1', '1296.gy1', '1296.gz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.432.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.gz1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712970
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ec1', '144.ef1', '216.r1'], 'contains': ['864.bn1', '864.eh1', '864.fc1', '1296.fv1', '1296.gx1', '1296.gz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684725, 1174327, 39366316080, 6227827207, 104], 'label': '46656.ir.432.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '432.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ha1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712971
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.n1', '12.bf1', '12.bg1', '12.bh1', '12.bi1', '12.bj1'], 'contains': ['48.o1', '48.r1', '48.bh1', '48.bj1', '48.bx1', '72.ct1', '72.du1', '72.dv1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 7, 269279866800], 'label': '46656.ir.24.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216712972
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ee1', '144.ef1', '216.s1', '216.gf1', '216.il1'], 'contains': ['864.bq1', '864.ek1', '864.fe1', '1296.fw1', '1296.gx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1174327, 39366316080, 325, 6227827207, 104], 'label': '46656.ir.432.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hb1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712973
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eg1', '144.eu1', '216.ey1'], 'contains': ['864.bl1', '864.ff1', '864.gx1', '1296.fy1', '1296.ha1', '1296.hb1', '1296.hc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387999647280, 93536397441, 6227827200, 387999647384, 41091127], 'label': '46656.ir.432.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '432.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hc1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712974
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eg1'], 'contains': ['864.bp1', '864.fg1', '864.hc1', '1296.gb1', '1296.ha1', '1296.hc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [325, 724820544270, 6227827200, 382729979624, 41091127], 'label': '46656.ir.432.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hd1', 'old_label': '432.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hd1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712975
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fh1', '144.eg1', '216.fx1'], 'contains': ['864.br1', '864.fh1', '864.hg1', '1296.gd1', '1296.ha1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [325, 174452060430, 6227827200, 104, 41091127], 'label': '46656.ir.432.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.he1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712976
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eh1', '144.ej1', '144.el1', '216.cb1', '216.ez1', '216.ip1'], 'contains': ['864.bi1', '864.fk1', '864.ge1', '1296.fx1', '1296.hd1', '1296.he1', '1296.hh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268280812800, 40323593955, 40323593520, 6227827200, 41091127], 'label': '46656.ir.432.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hf1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712977
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ei1', '144.ej1', '144.em1', '216.q1', '216.fa1', '216.it1'], 'contains': ['864.bj1', '864.fn1', '864.gf1', '1296.fz1', '1296.hd1', '1296.hf1', '1296.hi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 6227827200, 41091127], 'label': '46656.ir.432.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712978
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ej1', '144.ek1', '144.en1', '144.eu1', '216.fb1'], 'contains': ['864.bk1', '864.fo1', '864.gg1', '1296.fy1', '1296.hd1', '1296.hg1', '1296.hj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593955, 40323593520, 269279866800, 6227827200, 41091127], 'label': '46656.ir.432.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '432.hh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hh1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712979
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ei1', '144.ek1', '144.el1', '216.iq1'], 'contains': ['864.bm1', '864.fr1', '864.gh1', '1296.ga1', '1296.hd1', '1296.hh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [294706903784, 381772702405, 40323593520, 6227827200, 41091127], 'label': '46656.ir.432.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '432.hi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hi1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712980
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eh1', '144.ek1', '144.em1', '216.r1'], 'contains': ['864.bn1', '864.fs1', '864.gi1', '1296.gc1', '1296.hd1', '1296.hi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 40323593520, 6227827200, 34096648645, 41091127], 'label': '46656.ir.432.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '432.hj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hj1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712981
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eh1', '144.ei1', '144.ek1', '144.en1'], 'contains': ['864.bo1', '864.ft1', '864.gj1', '1296.gb1', '1296.hd1', '1296.hj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [40323593624, 40323593520, 6227827200, 41091127, 269279867125], 'label': '46656.ir.432.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hk1', 'old_label': '432.hk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hk1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712982
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '12.bk1'], 'contains': ['48.p1', '48.q1', '48.t1', '48.bk1', '48.bo1', '48.bp1', '48.ci1', '72.cu1', '72.de1', '72.dh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 325, 270715782960, 40323593520, 6227827207, 461482882830], 'label': '46656.ir.24.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '24.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216712983
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.el1', '144.em1', '144.en1', '216.s1', '216.fy1', '216.ir1'], 'contains': ['864.bq1', '864.fw1', '864.gk1', '1296.gd1', '1296.hd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 6227827200, 41091127], 'label': '46656.ir.432.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.hl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hl1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216712984
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eh1', '144.ej1', '216.cc1'], 'contains': ['864.bs1', '864.fx1', '864.gl1', '1296.gf1', '1296.he1', '1296.hi1', '1296.hj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1481684835, 268280812800, 40323593520, 6227827200, 41091127], 'label': '46656.ir.432.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '432.hm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hm1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712985
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ei1', '144.ej1', '216.iu1'], 'contains': ['864.bt1', '864.fz1', '864.gm1', '1296.gh1', '1296.hf1', '1296.hh1', '1296.hj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 1481684400, 6227827200, 41091127, 270715783395], 'label': '46656.ir.432.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iu1', 'old_label': '432.hn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hn1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712986
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ej1', '144.ev1', '216.cd1', '216.dq1', '216.iv1'], 'contains': ['864.bu1', '864.ga1', '864.gn1', '1296.ge1', '1296.he1', '1296.hf1', '1296.hg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 6227827200, 41091127], 'label': '46656.ir.432.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.ho1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ho1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216712987
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ej1', '144.ek1', '144.ew1'], 'contains': ['864.bv1', '864.gb1', '864.go1', '1296.gg1', '1296.hg1', '1296.hh1', '1296.hi1', '1296.hj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [1481684504, 40323593520, 269279866800, 6227827200, 41091127], 'label': '46656.ir.432.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hp1', 'old_label': '432.hp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hp1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712988
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eh1', '144.ei1', '144.ek1'], 'contains': ['864.bw1', '864.gd1', '864.gt1', '1296.gi1', '1296.hh1', '1296.hi1', '1296.hj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [381772702405, 40323593520, 6227827200, 382729979624, 41091127], 'label': '46656.ir.432.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq1', 'old_label': '432.hq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hq1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712989
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.eh1', '144.ei1', '144.ek1'], 'contains': ['864.bw2', '864.gd2', '864.gt2', '1296.gi2', '1296.hh1', '1296.hi1', '1296.hj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [40323593520, 6227827200, 382729979624, 41091127, 269279867125], 'label': '46656.ir.432.hq2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq2', 'old_label': '432.hq2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hq2', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216712990
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.eo1', '144.eq1', '216.ce1', '216.fc1', '216.ip1'], 'contains': ['864.bb1', '864.bi1', '864.ck1', '1296.gj1', '1296.hk1', '1296.hl1', '1296.hm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 6227827200, 104], 'label': '46656.ir.432.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '432.hr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216712992
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eo1', '144.er1', '216.t1', '216.gf1', '216.ir1'], 'contains': ['864.bh1', '864.bq1', '864.cp1', '1296.gl1', '1296.hk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174320, 6227827200, 104, 1174645], 'label': '46656.ir.432.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.ht1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ht1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216712993
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['11664.bj1', '11664.r1', '11664.u1', '11664.e1', '11664.bk1', '11664.b1', '11664.s1', '11664.x1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.e1', '2.f1'], 'contains': ['8.b1', '12.bz1', '16.h1', '36.cc1', '108.fa1'], 'core': '4.i1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6267744618, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': ['2.c1', '2.e1', '2.f1'], 'normal_contains': ['8.b1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '46656.ir', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216712994
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1', '12.bk1'], 'contains': ['48.p1', '48.z1', '48.ba1', '72.dq1', '72.ds1', '216.dx1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [270715782960, 40323593624, 40323593520, 6227827207, 499, 7, 325, 461482882830], 'label': '46656.ir.24.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '24.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216712995
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ep1', '144.eq1', '144.er1', '216.u1', '216.dc1', '216.fd1', '216.it1', '216.ix1', '216.iy1', '216.jb1'], 'contains': ['864.bj1', '864.cq1', '1296.hk1', '1296.hn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6227827200], 'label': '46656.ir.432.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '432.hu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hu1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712996
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ep1', '144.eq1', '216.dd1', '216.iu1', '216.iz1'], 'contains': ['864.bt1', '864.cr1', '1296.hm1', '1296.hn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227827200, 270715783395], 'label': '46656.ir.432.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '432.hv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hv1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712997
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.er1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eq1', '216.cf1', '216.de1', '216.dv1', '216.iv1', '216.iw1', '216.ja1', '216.jc1'], 'contains': ['864.bu1', '864.cs1', '1296.hl1', '1296.hn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.432.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.hw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hw1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216712998
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.es1', '144.et1', '216.dw1'], 'contains': ['864.bx1', '864.ch1', '864.dj1', '1296.go1', '1296.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091120, 624302466480, 270715782960, 40323593520, 6227827200], 'label': '46656.ir.432.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '432.hx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hx1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216712999
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.eu1', '144.ev1', '144.ew1', '216.dw1'], 'contains': ['864.bx1', '864.fi1', '864.gp1', '1296.hb1', '1296.hg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [624302466480, 270715782960, 40323593520, 6227827200, 41091127], 'label': '46656.ir.432.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '432.hy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hy1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713000
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bq1', '144.ex1', '216.fx1'], 'contains': ['864.by1', '864.eq1', '864.hg1', '1296.hp1', '1296.hq1', '1296.hr1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 325, 174452060430, 6227827207, 104], 'label': '46656.ir.432.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.hz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.hz1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713001
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ey1', '144.fa1', '216.f1', '216.v1', '216.ch1'], 'contains': ['864.cb1', '864.du1', '864.fd1', '1296.ho1', '1296.hs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 325, 31658054504, 39957127, 37885034880], 'label': '46656.ir.432.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '432.ia1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ia1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713002
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ey1', '144.ez1', '216.g1', '216.ie1', '216.il1'], 'contains': ['864.cd1', '864.dv1', '864.fe1', '1296.ho1', '1296.ht1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 387037284480, 325, 39957127, 104], 'label': '46656.ir.432.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.ib1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ib1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713003
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ez1', '144.fa1', '216.v1', '216.bs1', '216.if1', '216.jd1'], 'contains': ['864.cb1', '864.dw1', '864.ev1', '1296.ho1', '1296.hu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 325, 1481684400, 1481684504, 39957127], 'label': '46656.ir.432.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.ic1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ic1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713004
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ex1', '144.fc1', '216.ey1'], 'contains': ['864.bz1', '864.ef1', '864.gx1', '1296.hp1', '1296.hw1', '1296.hy1', '1296.hz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 387999647280, 325, 6227827207, 568299191498], 'label': '46656.ir.432.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '432.id1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.id1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713005
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1', '12.bk1'], 'contains': ['48.p1', '48.bb1', '48.bc1', '72.dr1', '72.dt1', '216.dy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091619, 7, 325, 270715782960, 40323593520, 6227827207, 461482882830], 'label': '46656.ir.24.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '24.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216713006
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ex1', '144.fd1'], 'contains': ['864.ca1', '864.eg1', '864.gy1', '1296.hq1', '1296.hw1', '1296.hz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [41091120, 174564513075, 387999647280, 6227827207, 387999647384], 'label': '46656.ir.432.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ie1', 'old_label': '432.ie1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ie1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713007
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fb1', '144.fe1', '216.ci1', '216.fj1', '216.if1'], 'contains': ['864.cb1', '864.ei1', '864.hd1', '1296.hr1', '1296.hv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 268280812800, 325, 355419187304, 6227827207], 'label': '46656.ir.432.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '432.if1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.if1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713008
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ex1', '144.fb1', '144.fg1', '216.fk1'], 'contains': ['864.cc1', '864.ej1', '864.he1', '1296.hr1', '1296.hw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 387999647280, 325, 6227827207, 387999647384], 'label': '46656.ir.432.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.ig1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ig1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713009
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fb1', '144.ff1', '216.w1', '216.fl1', '216.il1'], 'contains': ['864.cd1', '864.ek1', '864.hf1', '1296.hr1', '1296.hx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 6227827207, 104], 'label': '46656.ir.432.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.ih1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ih1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713010
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fe1', '144.ff1', '144.fg1', '216.w1', '216.fy1', '216.ie1'], 'contains': ['864.cd1', '864.ep1', '864.gk1', '1296.hr1', '1296.ia1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091120, 325, 40323593520, 6227827207], 'label': '46656.ir.432.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.ii1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ii1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713011
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ey1', '144.fh1', '216.c1', '216.cl1', '216.im1'], 'contains': ['864.cf1', '864.dn1', '864.fb1', '1296.hs1', '1296.ht1', '1296.ib1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 268280812800, 39957127, 37885034880, 31658054835], 'label': '46656.ir.432.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.ij1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ij1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713012
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ez1', '144.fh1', '216.bp1', '216.ig1', '216.in1'], 'contains': ['864.ce1', '864.dq1', '864.er1', '1296.ht1', '1296.hu1', '1296.ic1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 1481684835, 301891126320, 1481684400, 39957127], 'label': '46656.ir.432.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.ik1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ik1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713013
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fa1', '144.fh1', '216.x1', '216.bq1', '216.cl1'], 'contains': ['864.cf1', '864.ds1', '864.eu1', '1296.hs1', '1296.hu1', '1296.id1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684835, 1481684400, 39957127], 'label': '46656.ir.432.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.il1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.il1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713014
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fb1', '144.fi1', '216.cm1', '216.ex1', '216.in1'], 'contains': ['864.ce1', '864.dx1', '864.gu1', '1296.hv1', '1296.hw1', '1296.hx1', '1296.ie1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 6227827207, 435], 'label': '46656.ir.432.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.im1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.im1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713015
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fe1', '144.fi1', '216.cm1', '216.ez1', '216.ig1'], 'contains': ['864.ce1', '864.ea1', '864.ge1', '1296.hv1', '1296.ia1', '1296.if1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 268280812800, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.432.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.in1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.in1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713016
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1', '12.bk1'], 'contains': ['48.q1', '48.z1', '48.bb1', '72.dw1', '72.eg1', '216.dz1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091120, 499, 7, 325, 270715782960, 40323593520, 461482882830], 'label': '46656.ir.24.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '24.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216713017
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ff1', '144.fi1', '216.y1', '216.fa1', '216.im1'], 'contains': ['864.cf1', '864.ec1', '864.gf1', '1296.hx1', '1296.ia1', '1296.ig1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684835, 1481684400, 6227827207], 'label': '46656.ir.432.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.io1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.io1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713018
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fc1', '144.fd1', '144.fg1', '144.fi1', '216.fb1'], 'contains': ['864.cg1', '864.ed1', '864.gg1', '1296.hw1', '1296.ia1', '1296.ih1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 40323593955, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.432.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '432.ip1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ip1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713019
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fc1', '144.fj1', '216.dw1'], 'contains': ['864.ch1', '864.el1', '864.gp1', '1296.hy1', '1296.ih1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 624302466480, 270715782960, 40323593520, 6227827207], 'label': '46656.ir.432.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '432.iq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iq1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713020
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fc1', '144.fd1', '144.fk1'], 'contains': ['864.ci1', '864.em1', '864.gq1', '1296.hz1', '1296.ih1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [41091120, 270715782960, 40323593520, 6227827207, 457175462064], 'label': '46656.ir.432.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ir1', 'old_label': '432.ir1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ir1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713021
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fh1', '216.bi1', '216.cn1', '216.io1', '216.je1'], 'contains': ['864.a1', '864.dp1', '864.ez1', '1296.ib1', '1296.ic1', '1296.id1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 269279866800, 39957127], 'label': '46656.ir.432.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.is1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.is1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713022
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fi1', '144.fj1', '144.fk1', '216.co1', '216.dq1', '216.io1'], 'contains': ['864.a1', '864.dz1', '864.gn1', '1296.ie1', '1296.if1', '1296.ig1', '1296.ih1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.432.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.it1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.it1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713023
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fl1', '216.bd1', '216.ca1', '216.gs1', '216.jf1', '216.jg1', '216.jh1', '216.ju1'], 'contains': ['864.cj1', '864.da1', '1296.ii1', '1296.ij1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 355419187304, 1174645, 6267744000], 'label': '46656.ir.432.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.iu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iu1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216713024
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fo1', '216.bb1', '216.ch1', '216.ih1', '216.jf1', '216.ji1', '216.jj1', '216.jv1'], 'contains': ['864.cj1', '864.du1', '1296.ik1', '1296.io1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39957120, 325, 1481684400, 1521641624], 'label': '46656.ir.432.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.iv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iv1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713025
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fm1', '144.fn1', '216.be1', '216.bs1', '216.ii1', '216.jg1', '216.jk1', '216.jl1', '216.jv1'], 'contains': ['864.cj1', '864.dw1', '864.fu1', '1296.il1', '1296.im1', '1296.in1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 1134007, 325, 1481684400, 1521641624], 'label': '46656.ir.432.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.iw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713026
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fp1', '216.bf1', '216.ci1', '216.fw1', '216.jg1', '216.ji1', '216.jm1', '216.jw1'], 'contains': ['864.cj1', '864.ei1', '1296.ip1', '1296.iq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 355419187304, 6227827207, 1174645], 'label': '46656.ir.432.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.ix1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ix1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713027
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1', '12.bk1'], 'contains': ['48.q1', '48.ba1', '48.bc1', '72.dx1', '72.eh1', '216.ea1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 325, 270715782960, 6227827818, 40323593520, 461482882830], 'label': '46656.ir.24.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '24.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216713028
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fq1', '216.be1', '216.ch1', '216.hn1', '216.ij1', '216.jh1', '216.jm1', '216.jn1'], 'contains': ['864.cj1', '864.fd1', '1296.ir1', '1296.is1', '1296.it1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050807, 39957120, 325, 1481684400, 1521641624], 'label': '46656.ir.432.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.iy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iy1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216713029
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fr1', '216.bg1', '216.ci1', '216.gs1', '216.ii1', '216.jj1', '216.jn1', '216.jx1'], 'contains': ['864.cj1', '864.hd1', '1296.iu1', '1296.iv1', '1296.iw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 1174320, 355419187304, 1174645], 'label': '46656.ir.432.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.iz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.iz1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216713030
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ja1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1', '216.bc1', '216.cj1', '216.gu1', '216.ji1', '216.jk1', '216.jn1', '216.ju1'], 'contains': ['864.cj1', '1296.ix1', '1296.jb1', '1296.jd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 6227464320, 1174320, 355419187304, 1174645], 'label': '46656.ir.432.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.ja1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ja1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216713031
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1', '216.bd1', '216.cj1', '216.gx1', '216.ik1', '216.jj1', '216.jl1', '216.jm1'], 'contains': ['864.cj1', '1296.iy1', '1296.je1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 268280812800, 1174320, 355419187304, 1174645], 'label': '46656.ir.432.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.jb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jb1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216713032
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1', '216.bf1', '216.ck1', '216.gu1', '216.ih1', '216.jh1', '216.jl1', '216.jx1'], 'contains': ['864.cj1', '1296.iz1', '1296.jf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 6227464327, 355419187304, 1174645], 'label': '46656.ir.432.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.jc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jc1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713033
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1', '216.bg1', '216.ck1', '216.gx1', '216.ij1', '216.jf1', '216.jk1', '216.jw1'], 'contains': ['864.cj1', '1296.ja1', '1296.jc1', '1296.jg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 355419187304, 1174645], 'label': '46656.ir.432.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.jd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jd1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216713034
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fl1', '144.fs1', '216.t1', '216.hd1', '216.jo1'], 'contains': ['864.cp1', '864.ct1', '864.dc1', '1296.ii1', '1296.jh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174320, 104, 1174645, 6267744000], 'label': '46656.ir.432.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.je1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.je1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713035
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fl1', '144.ft1', '216.ce1', '216.fe1', '216.jq1'], 'contains': ['864.ck1', '864.cu1', '864.de1', '1296.ij1', '1296.jh1', '1296.ji1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 104, 6267744000], 'label': '46656.ir.432.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '432.jf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jf1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713036
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fm1', '144.fv1', '216.bp1', '216.ip1', '216.jq1'], 'contains': ['864.ck1', '864.dq1', '864.fk1', '1296.il1', '1296.jk1', '1296.jl1', '1296.jo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [301891126320, 39957120, 1134007, 1481684400, 1521641624], 'label': '46656.ir.432.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.jg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jg1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713037
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fn1', '144.fu1', '216.cw1'], 'contains': ['864.cl1', '864.dr1', '864.fm1', '1296.im1', '1296.jj1', '1296.jm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39957120, 1134007, 325, 37885034880, 1521641624], 'label': '46656.ir.432.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '432.jh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jh1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713038
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '12.i1', '12.be1'], 'contains': ['48.a1', '48.v1', '48.x1', '72.dz1', '72.ed1', '72.ee1', '216.ec1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 39957619], 'label': '46656.ir.24.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713039
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fn1', '144.fv1', '216.bq1', '216.cx1', '216.kt1'], 'contains': ['864.cm1', '864.ds1', '864.fn1', '1296.il1', '1296.jj1', '1296.jm1', '1296.jn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 39957120, 1134007, 1481684400, 1521641624], 'label': '46656.ir.432.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.ji1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ji1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713040
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fm1', '144.fu1', '216.iq1'], 'contains': ['864.cn1', '864.dt1', '864.fr1', '1296.im1', '1296.jk1', '1296.jo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1481684725, 387037284480, 39957120, 1134007, 39957224], 'label': '46656.ir.432.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '432.jj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jj1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713041
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fn1', '144.fw1', '216.f1', '216.cy1', '216.jv1'], 'contains': ['864.co1', '864.du1', '864.fu1', '1296.in1', '1296.jj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 1134007, 325, 31697930984, 37885034880], 'label': '46656.ir.432.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '432.jk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jk1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713042
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fm1', '144.fw1', '216.g1', '216.ir1', '216.jo1'], 'contains': ['864.cp1', '864.dv1', '864.fw1', '1296.in1', '1296.jk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 39957120, 1134007, 325, 39957224], 'label': '46656.ir.432.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.jl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jl1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713043
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fo1', '144.fx1', '216.cl1', '216.cu1', '216.kt1'], 'contains': ['864.cm1', '864.dn1', '864.ds1', '1296.ik1', '1296.jp1', '1296.jq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 1521641955, 39957120, 1481684400], 'label': '46656.ir.432.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.jm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713044
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fo1', '144.fy1', '216.v1', '216.cv1', '216.jv1'], 'contains': ['864.co1', '864.du1', '864.dw1', '1296.io1', '1296.jq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39957120, 325, 31697930984, 37885034880], 'label': '46656.ir.432.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '432.jn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jn1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713045
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fp1', '144.fz1', '216.cm1', '216.fc1', '216.jq1'], 'contains': ['864.ck1', '864.dx1', '864.ea1', '1296.ip1', '1296.jr1', '1296.js1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 6227827207, 435], 'label': '46656.ir.432.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.jo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jo1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713046
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fp1', '144.ga1', '216.w1', '216.gf1', '216.jo1'], 'contains': ['864.cp1', '864.ek1', '864.ep1', '1296.iq1', '1296.js1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174320, 6227827207, 104, 1174645], 'label': '46656.ir.432.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.jp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jp1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713047
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '144.gb1', '216.cw1'], 'contains': ['864.cl1', '864.et1', '864.fa1', '1296.is1', '1296.jt1', '1296.ju1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41050807, 39957120, 39366316405, 31697930984, 37885034880], 'label': '46656.ir.432.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '432.jq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jq1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713048
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fq1', '144.gc1', '216.cl1', '216.cx1', '216.fi1'], 'contains': ['864.cm1', '864.eu1', '864.fb1', '1296.ir1', '1296.jt1', '1296.ju1', '1296.jv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 1481684400, 1521641624], 'label': '46656.ir.432.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '432.jr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jr1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713049
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1', '12.j1', '12.bd1', '12.be1'], 'contains': ['48.a1', '48.w1', '48.y1', '72.ea1', '72.eb1', '72.ef1', '72.eh1', '216.ed1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 7, 6227827818, 325, 269279866800], 'label': '46656.ir.24.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216713050
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fq1', '144.gd1', '216.v1', '216.cy1', '216.hn1'], 'contains': ['864.co1', '864.ev1', '864.fd1', '1296.it1', '1296.jt1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41050807, 39957120, 325, 31697930984, 37885034880], 'label': '46656.ir.432.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '432.js1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.js1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713051
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fr1', '144.gf1', '216.cm1', '216.fe1', '216.ip1'], 'contains': ['864.ck1', '864.ge1', '864.gu1', '1296.iu1', '1296.jw1', '1296.jx1', '1296.jy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 1174320, 435], 'label': '46656.ir.432.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.jt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jt1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713052
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fr1', '144.ge1', '216.iq1'], 'contains': ['864.cn1', '864.gh1', '864.hb1', '1296.iv1', '1296.jw1', '1296.jy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 268281987445, 39366316080, 1174320, 355419187304], 'label': '46656.ir.432.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '432.ju1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ju1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713053
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fr1', '144.gg1', '216.w1', '216.hd1', '216.ir1'], 'contains': ['864.cp1', '864.gk1', '864.hf1', '1296.iw1', '1296.jw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 104, 1174645], 'label': '46656.ir.432.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.jv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713054
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '216.cg1', '216.hm1', '216.is1', '216.jp1', '216.jr1', '216.js1', '216.jt1'], 'contains': ['1296.jz1', '1296.ka1', '1296.kb1', '1728.t1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 174452060430], 'label': '46656.ir.432.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.jw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jw1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 216713055
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gr1', '216.cz1', '216.hn1', '216.ik1', '216.ju1', '216.jv1', '216.jw1', '216.jx1'], 'contains': ['864.cj1', '864.co1', '1296.kb1', '1296.kc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 31697930984, 37885034880], 'label': '46656.ir.432.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '432.jx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jx1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216713056
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fs1', '144.ft1', '216.u1', '216.df1', '216.ff1', '216.jy1', '216.jz1', '216.ka1', '216.ks1'], 'contains': ['864.cq1', '864.cw1', '1296.jh1', '1296.kd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6267744000], 'label': '46656.ir.432.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '432.jy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jy1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713057
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ft1', '216.cf1', '216.dg1', '216.ee1', '216.kb1', '216.kc1', '216.kd1', '216.kw1'], 'contains': ['864.cs1', '864.di1', '1296.ji1', '1296.kd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 269279866800, 6267744000], 'label': '46656.ir.432.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.jz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.jz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713058
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fu1', '144.fv1', '144.fw1', '216.c1', '216.dh1', '216.it1', '216.jy1', '216.ke1', '216.kf1', '216.kt1'], 'contains': ['864.cq1', '864.dn1', '864.fn1', '1296.jj1', '1296.jk1', '1296.ke1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 39957120, 1134007, 31697930984, 37885034880], 'label': '46656.ir.432.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.ka1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ka1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713059
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fu1', '144.fv1', '216.di1', '216.iu1', '216.kg1'], 'contains': ['864.cr1', '864.do1', '864.fz1', '1296.jm1', '1296.jo1', '1296.ke1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1521641955, 268280812800, 39957120, 1134007, 37885034880], 'label': '46656.ir.432.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '432.kb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713060
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.o1', '12.bl1', '12.bm1', '12.bn1', '12.bo1', '12.bx1'], 'contains': ['48.r1', '48.s1', '48.bu1', '48.bz1', '48.cj1', '72.cv1', '72.ei1', '72.er1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.24.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713061
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fv1', '216.bi1', '216.dj1', '216.iv1', '216.kb1', '216.kh1', '216.ki1', '216.kx1'], 'contains': ['864.cs1', '864.dp1', '864.ga1', '1296.jl1', '1296.jn1', '1296.ke1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 1134007, 1481684400, 269279866800], 'label': '46656.ir.432.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.kc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kc1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713062
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fx1', '216.cn1', '216.da1', '216.iw1', '216.kc1', '216.kj1', '216.kk1', '216.kx1'], 'contains': ['864.cs1', '864.dp1', '1296.jp1', '1296.kf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 1481684400, 269279866800], 'label': '46656.ir.432.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.kd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kd1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713063
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fx1', '144.fy1', '216.x1', '216.db1', '216.ix1', '216.jz1', '216.kl1', '216.km1', '216.kt1'], 'contains': ['864.cq1', '864.ds1', '1296.jq1', '1296.kf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 31697930984, 37885034880], 'label': '46656.ir.432.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '432.ke1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ke1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713064
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fz1', '216.co1', '216.dk1', '216.dv1', '216.kb1', '216.kj1', '216.kn1', '216.ky1'], 'contains': ['864.cs1', '864.dz1', '1296.jr1', '1296.kg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.432.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.kf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kf1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713065
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fz1', '144.ga1', '216.y1', '216.dl1', '216.fd1', '216.jy1', '216.kl1', '216.ko1', '216.ku1'], 'contains': ['864.cq1', '864.ec1', '1296.js1', '1296.kg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6227827207], 'label': '46656.ir.432.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '432.kg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713066
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gb1', '144.gc1', '144.gd1', '216.x1', '216.dh1', '216.fi1', '216.iy1', '216.ka1', '216.ko1', '216.kp1'], 'contains': ['864.cq1', '864.eu1', '1296.jt1', '1296.kh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 31697930984, 37885034880], 'label': '46656.ir.432.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.kh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713067
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gb1', '144.gc1', '216.di1', '216.iz1', '216.kq1'], 'contains': ['864.cr1', '864.ey1', '1296.ju1', '1296.kh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 37885034880, 1521641624], 'label': '46656.ir.432.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '432.ki1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ki1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713068
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gc1', '216.cn1', '216.dj1', '216.ep1', '216.ja1', '216.kd1', '216.kn1', '216.kr1'], 'contains': ['864.cs1', '864.ez1', '1296.jv1', '1296.kh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 1481684400, 269279866800], 'label': '46656.ir.432.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.kj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kj1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713069
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ge1', '144.gf1', '144.gg1', '216.y1', '216.dm1', '216.ff1', '216.it1', '216.km1', '216.kp1', '216.kv1'], 'contains': ['864.cq1', '864.gf1', '1296.jw1', '1296.ki1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504], 'label': '46656.ir.432.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.kk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kk1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713070
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ge1', '144.gf1', '216.dn1', '216.iu1', '216.kq1'], 'contains': ['864.cr1', '864.gm1', '1296.jy1', '1296.ki1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 270715783395], 'label': '46656.ir.432.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '432.kl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kl1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713071
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.g1', '12.p1', '12.bf1', '12.bl1', '12.bp1', '12.bq1'], 'contains': ['48.b1', '48.r1', '48.x1', '72.ej1', '72.en1', '72.es1', '216.ef1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 499, 7, 325, 269279866800, 1521641624], 'label': '46656.ir.24.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713072
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gf1', '216.co1', '216.do1', '216.ee1', '216.iv1', '216.kk1', '216.kr1', '216.kz1'], 'contains': ['864.cs1', '864.gn1', '1296.jx1', '1296.ki1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 269279866800], 'label': '46656.ir.432.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.km1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.km1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713073
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gh1', '144.gj1', '144.gn1', '216.z1', '216.dc1', '216.fg1', '216.ke1', '216.kl1', '216.kp1', '216.ks1'], 'contains': ['864.cq1', '1296.kj1', '3888.fd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1481684835, 6227464320, 1174320, 1481684400], 'label': '46656.ir.432.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '432.kn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kn1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713074
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gk1', '144.go1', '216.z1', '216.df1', '216.fh1', '216.jb1', '216.kf1', '216.km1', '216.ko1'], 'contains': ['864.cq1', '1296.kk1', '3888.fe1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504], 'label': '46656.ir.432.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '432.ko1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ko1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713075
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gl1', '144.gp1', '216.ba1', '216.dl1', '216.fg1', '216.ix1', '216.ka1', '216.kf1', '216.kv1'], 'contains': ['864.cq1', '1296.kl1', '3888.ff1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6227464327], 'label': '46656.ir.432.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '432.kp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713076
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gi1', '144.gm1', '144.gq1', '216.ba1', '216.dm1', '216.fh1', '216.iy1', '216.jz1', '216.ke1', '216.ku1'], 'contains': ['864.cq1', '1296.km1', '3888.fg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 6267381127, 1481684835, 1174320, 1481684400], 'label': '46656.ir.432.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '432.kq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kq1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713077
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gh1', '144.gj1', '216.dd1', '216.kg1', '216.kq1'], 'contains': ['864.cr1', '1296.kj1', '3888.fl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 6227464320, 1174320, 1481684400, 270715783395], 'label': '46656.ir.432.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '432.kr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kr1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713078
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gi1', '144.gm1', '216.dn1', '216.iz1', '216.kg1'], 'contains': ['864.cr1', '1296.km1', '3888.fm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 270715783395], 'label': '46656.ir.432.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '432.ks1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ks1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713079
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.er1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gj1', '216.cp1', '216.de1', '216.eg1', '216.kh1', '216.kj1', '216.kr1', '216.kw1'], 'contains': ['864.cs1', '1296.kj1', '3888.fh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6227464320, 1174320, 1481684400, 269279866800], 'label': '46656.ir.432.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.kt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kt1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713080
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gk1', '216.cp1', '216.dg1', '216.ej1', '216.jc1', '216.ki1', '216.kk1', '216.kn1'], 'contains': ['864.cs1', '1296.kk1', '3888.fi1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 269279866800], 'label': '46656.ir.432.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.ku1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ku1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713081
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gl1', '216.cq1', '216.dk1', '216.eg1', '216.iw1', '216.kd1', '216.ki1', '216.kz1'], 'contains': ['864.cs1', '1296.kl1', '3888.fj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227464327, 269279866800], 'label': '46656.ir.432.kv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.kv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kv1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713082
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.n1', '12.bp1', '12.br1', '12.bs1', '12.bt1', '12.bx1'], 'contains': ['48.r1', '48.ca1', '48.cc1', '72.cw1', '72.et1', '216.gu1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6227464327, 269279866800], 'label': '46656.ir.24.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713083
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gm1', '216.cq1', '216.do1', '216.ej1', '216.ja1', '216.kc1', '216.kh1', '216.ky1'], 'contains': ['864.cs1', '1296.km1', '3888.fk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 269279866800], 'label': '46656.ir.432.kw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '432.kw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kw1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713084
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gr1', '144.gs1', '216.dp1', '216.fi1', '216.jb1', '216.ks1', '216.kt1', '216.ku1', '216.kv1'], 'contains': ['864.cm1', '864.cq1', '1296.kc1', '1296.kn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 31697930984, 37885034880], 'label': '46656.ir.432.kx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '432.kx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kx1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713085
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gu1', '144.gv1', '216.d1', '216.il1', '216.jo1'], 'contains': ['864.ct1', '864.dv1', '864.ek1', '1296.ko1', '1296.kp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 6227827207, 104], 'label': '46656.ir.432.ky1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.ky1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ky1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713086
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gw1', '144.gx1', '144.gy1', '216.p1', '216.fy1', '216.jo1'], 'contains': ['864.ct1', '864.ep1', '864.fw1', '1296.kq1', '1296.kr1', '1296.ks1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 6227827207, 41091127], 'label': '46656.ir.432.kz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.kz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.kz1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713087
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gz1', '144.ha1', '216.p1', '216.hd1', '216.il1'], 'contains': ['864.ct1', '864.fe1', '864.hf1', '1296.kt1', '1296.ku1', '1296.kv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 6267744007, 1174327, 325, 40323593520], 'label': '46656.ir.432.la1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.la1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.la1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713088
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gu1', '144.hb1', '216.b1', '216.im1', '216.jy1'], 'contains': ['864.cw1', '864.dn1', '864.ec1', '1296.ko1', '1296.kw1', '1296.ky1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.432.lb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.lb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713089
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gv1', '144.hb1', '216.bn1', '216.in1', '216.jq1'], 'contains': ['864.cu1', '864.dq1', '864.dx1', '1296.ko1', '1296.kx1', '1296.kz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 6227827207, 104], 'label': '46656.ir.432.lc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.lc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713090
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gu1', '144.hc1', '216.e1', '216.ie1', '216.jo1'], 'contains': ['864.dc1', '864.dv1', '864.ep1', '1296.kp1', '1296.ky1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 39916807, 325, 40323593520, 6227827207], 'label': '46656.ir.432.ld1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '432.ld1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ld1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713091
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gv1', '144.hc1', '216.br1', '216.if1', '216.jg1'], 'contains': ['864.da1', '864.dw1', '864.ei1', '1296.kp1', '1296.kz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 268280812800, 325, 355419187304, 6227827207], 'label': '46656.ir.432.le1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '432.le1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.le1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713092
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gw1', '144.he1', '216.bx1', '216.ez1', '216.jq1'], 'contains': ['864.cu1', '864.ea1', '864.fk1', '1296.kq1', '1296.la1', '1296.ld1', '1296.le1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268280812800, 40323593955, 40323593520, 6227827207, 41091127], 'label': '46656.ir.432.lf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.lf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lf1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713093
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.g1', '12.q1', '12.bg1', '12.bm1', '12.br1', '12.bu1'], 'contains': ['48.c1', '48.r1', '48.v1', '72.ek1', '72.eo1', '72.eu1', '216.eh1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 325, 1481684400, 269279866800, 1134499, 1521641624], 'label': '46656.ir.24.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713094
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gw1', '144.hd1', '216.by1'], 'contains': ['864.cv1', '864.eb1', '864.fl1', '1296.kr1', '1296.la1', '1296.le1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [268280812800, 294706903784, 301891126645, 6227827207, 41091127], 'label': '46656.ir.432.lg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '432.lg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lg1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713095
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gx1', '144.he1', '216.q1', '216.fa1', '216.jy1'], 'contains': ['864.cw1', '864.ec1', '864.fn1', '1296.kq1', '1296.lc1', '1296.lf1', '1296.li1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 6227827207, 41091127], 'label': '46656.ir.432.lh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.lh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lh1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713096
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gy1', '144.he1', '144.hg1', '216.fb1'], 'contains': ['864.cx1', '864.ed1', '864.fo1', '1296.kq1', '1296.lb1', '1296.lg1', '1296.lh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 40323593520, 269279866800, 6227827207, 41091127], 'label': '46656.ir.432.li1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '432.li1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.li1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713097
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gy1', '144.hd1', '144.hh1'], 'contains': ['864.cy1', '864.ee1', '864.fq1', '1296.kr1', '1296.lb1', '1296.lh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [40323593624, 387999647280, 325, 6227827207, 41091127], 'label': '46656.ir.432.lj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.lj1', 'old_label': '432.lj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lj1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713098
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gx1', '144.hd1', '216.r1'], 'contains': ['864.cz1', '864.eh1', '864.fs1', '1296.kr1', '1296.lc1', '1296.li1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1481684725, 39366316080, 6227827207, 104, 41091127], 'label': '46656.ir.432.lk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '432.lk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lk1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713099
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gw1', '144.hf1', '216.bz1', '216.fj1', '216.jg1'], 'contains': ['864.da1', '864.ei1', '864.fu1', '1296.ks1', '1296.la1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 325, 355419187304, 6227827207, 41091127], 'label': '46656.ir.432.ll1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '432.ll1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ll1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713100
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gy1', '144.hf1', '144.hi1', '216.fk1'], 'contains': ['864.db1', '864.ej1', '864.fv1', '1296.ks1', '1296.lb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [387999647280, 325, 6227827207, 387999647384, 41091127], 'label': '46656.ir.432.lm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '432.lm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lm1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713101
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gx1', '144.hf1', '216.s1', '216.fl1', '216.jo1'], 'contains': ['864.dc1', '864.ek1', '864.fw1', '1296.ks1', '1296.lc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 325, 6227827207, 104, 41091127], 'label': '46656.ir.432.ln1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.ln1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ln1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713102
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fk1', '144.hi1', '216.fx1'], 'contains': ['864.dd1', '864.eq1', '864.fh1', '1296.ks1', '1296.lj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [325, 174452060430, 6227827207, 104, 41091127], 'label': '46656.ir.432.lo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '432.lo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lo1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713103
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gz1', '144.hk1', '216.bx1', '216.fe1', '216.in1'], 'contains': ['864.cu1', '864.er1', '864.gu1', '1296.kt1', '1296.lk1', '1296.ll1', '1296.lm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 1174327, 268280812800, 40323593955, 40323593520], 'label': '46656.ir.432.lp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.lp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lp1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713104
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['11664.l1', '11664.o1', '11664.p1', '11664.m1', '11664.bn1', '11664.q1', '11664.n1', '11664.bm1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.c1', '8.e1', '8.g1', '12.ca1', '12.cb1', '16.j1', '108.fh1'], 'core': '4.j1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 6227827200, 461482882830, 1521641624], 'label': '46656.ir.4.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.c1', '8.e1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '46656.ir', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216713105
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.i1', '12.p1', '12.bh1', '12.bn1', '12.bs1', '12.bv1'], 'contains': ['48.r1', '48.v1', '72.ep1', '72.ev1', '216.ei1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39917299, 39366316080, 39957120, 7, 325, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.24.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713106
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gz1', '144.hj1', '216.by1'], 'contains': ['864.cv1', '864.es1', '864.gv1', '1296.ku1', '1296.lk1', '1296.lm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 1174327, 268280812800, 294706903784, 301891126645], 'label': '46656.ir.432.lq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '432.lq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lq1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713107
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gz1', '144.hl1', '216.bz1', '216.gs1', '216.if1'], 'contains': ['864.da1', '864.ev1', '864.hd1', '1296.kv1', '1296.lk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 1174327, 268280812800, 325, 355419187304], 'label': '46656.ir.432.lr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '432.lr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lr1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713108
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ha1', '144.hk1', '216.q1', '216.ff1', '216.im1'], 'contains': ['864.cw1', '864.fb1', '864.gf1', '1296.kt1', '1296.ln1', '1296.lo1', '1296.lp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 1481684400, 1481684504], 'label': '46656.ir.432.ls1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '432.ls1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ls1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713109
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ha1', '144.hj1', '216.r1'], 'contains': ['864.cz1', '864.fc1', '864.gi1', '1296.ku1', '1296.ln1', '1296.lp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 1481684725, 1174327, 39366316080, 104], 'label': '46656.ir.432.lt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '432.lt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lt1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713110
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ha1', '144.hl1', '216.s1', '216.hd1', '216.ie1'], 'contains': ['864.dc1', '864.fe1', '864.gk1', '1296.kv1', '1296.ln1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 325, 104], 'label': '46656.ir.432.lu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '432.lu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713111
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hb1', '216.bh1', '216.io1', '216.kb1'], 'contains': ['864.di1', '864.dp1', '864.dz1', '1296.kw1', '1296.kx1', '1296.lq1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.432.lv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.lv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713112
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hb1', '144.hc1', '216.bo1', '216.ig1', '216.jq1'], 'contains': ['864.de1', '864.dq1', '864.ea1', '1296.ky1', '1296.kz1', '1296.lq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 268280812800, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.432.lw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '432.lw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lw1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713113
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hd1', '144.he1', '144.hf1', '216.cb1', '216.ex1', '216.jq1'], 'contains': ['864.de1', '864.dx1', '864.fk1', '1296.la1', '1296.lb1', '1296.lc1', '1296.lr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827207, 104, 41091127], 'label': '46656.ir.432.lx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.lx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lx1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713114
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ly1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hd1', '144.he1', '216.cc1'], 'contains': ['864.dh1', '864.dy1', '864.fx1', '1296.le1', '1296.lh1', '1296.li1', '1296.lr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 268280812800, 1481684504, 6227827207, 41091127], 'label': '46656.ir.432.ly1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '432.ly1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ly1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713115
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.lz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.he1', '144.hm1', '216.cd1', '216.dq1', '216.kb1'], 'contains': ['864.di1', '864.dz1', '864.ga1', '1296.ld1', '1296.lf1', '1296.lg1', '1296.lr1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 6227827207, 41091127], 'label': '46656.ir.432.lz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.lz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.lz1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713116
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.o1', '12.bj1', '12.bq1', '12.bu1', '12.bv1', '12.bw1'], 'contains': ['48.r1', '48.cb1', '48.cd1', '72.cx1', '72.ew1', '216.gx1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.24.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713117
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.ma1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hg1', '144.hh1', '144.hi1', '216.ey1'], 'contains': ['864.df1', '864.ef1', '864.ff1', '1296.lb1', '1296.lj1', '1296.ls1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387999647280, 325, 6227827207, 41091127, 568299191498], 'label': '46656.ir.432.ma1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '432.ma1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ma1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713118
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hg1', '144.hm1', '216.dw1'], 'contains': ['864.dj1', '864.el1', '864.fi1', '1296.lg1', '1296.ls1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [624302466480, 270715782960, 40323593520, 6227827207, 41091127], 'label': '46656.ir.432.mb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '432.mb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mb1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713119
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hg1', '144.hh1'], 'contains': ['864.dl1', '864.en1', '864.fj1', '1296.lh1', '1296.ls1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [40323593624, 387999647280, 132379435521, 6227827207, 41091127], 'label': '46656.ir.432.mc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.mc1', 'old_label': '432.mc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mc1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713120
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.md1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hj1', '144.hk1', '144.hl1', '216.cb1', '216.fe1', '216.ig1'], 'contains': ['864.de1', '864.er1', '864.ge1', '1296.lk1', '1296.ln1', '1296.lt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 268280812800, 435], 'label': '46656.ir.432.md1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '432.md1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.md1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713121
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.me1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hj1', '144.hk1', '216.cc1'], 'contains': ['864.dh1', '864.ew1', '864.gl1', '1296.lm1', '1296.lp1', '1296.lt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 1481684835, 268280812800], 'label': '46656.ir.432.me1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '432.me1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.me1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713122
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hk1', '216.cd1', '216.ee1', '216.io1'], 'contains': ['864.di1', '864.ez1', '864.gn1', '1296.ll1', '1296.lo1', '1296.lt1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 1481684400, 269279866800], 'label': '46656.ir.432.mf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '432.mf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mf1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713123
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cl1', '216.cr1', '216.hb1', '216.jd1'], 'contains': ['864.ev1', '1296.lu1', '3888.go1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 268280812800, 325, 355419187304, 6227752218], 'label': '46656.ir.432.mg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.o1', 'old_label': '432.mg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mg1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713124
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cm1', '216.cr1', '216.hc1', '216.jd1'], 'contains': ['864.ev1', '1296.lv1', '3888.gp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 6267669018, 268280812800, 325, 355419187304], 'label': '46656.ir.432.mh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.o1', 'old_label': '432.mh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mh1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713125
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cl1', '216.cs1'], 'contains': ['864.ex2', '1296.ly1', '3888.go1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [299935198184, 268280812800, 381772702405, 6227752218, 381771895687], 'label': '46656.ir.432.mi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '432.mi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mi1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713126
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '432.mj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cm1', '216.cs1'], 'contains': ['864.ex2', '1296.lz1', '3888.gp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267669018, 299935198184, 268280812800, 381772702405, 381771895687], 'label': '46656.ir.432.mj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '432.mj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.mj1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713127
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.r1', '12.bf1', '12.bm1', '12.bs1', '12.bw1', '12.by1'], 'contains': ['48.r1', '48.w1', '72.el1', '72.ex1', '216.ek1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6227827818, 269279866800], 'label': '46656.ir.24.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713130
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '162.a1', '162.m1'], 'contains': ['972.a1', '972.b1', '972.c1', '972.d1', '972.e1', '972.h1', '972.i1', '972.bz1', '972.ca1', '972.ch1', '972.ci1', '972.cj1', '972.ck1', '972.cy1', '972.cz1', '1458.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41050800, 499, 443130957804, 444, 269279866800, 40320], 'label': '46656.ir.486.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '486.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713131
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1', '54.t1', '243.b1'], 'contains': ['972.n1', '972.p1', '972.r1', '972.cb1', '972.cc1', '972.cq1', '972.cs1', '1458.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 499, 443130957804, 39916800, 37885034880], 'label': '46656.ir.486.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713132
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '54.u1', '243.b1'], 'contains': ['972.n1', '972.q1', '972.s1', '972.cd1', '972.ce1', '972.ct1', '972.cu1', '1458.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 443130957804, 39916800, 39957619, 37885034880], 'label': '46656.ir.486.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713133
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1', '54.v1', '243.b1'], 'contains': ['972.o1', '972.p1', '972.s1', '972.cm1', '972.cn1', '972.cr1', '972.cv1', '1458.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 499, 39916800, 443609999724, 37885034880], 'label': '46656.ir.486.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713134
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1', '54.w1', '243.b1'], 'contains': ['972.o1', '972.q1', '972.r1', '972.co1', '972.cp1', '972.cw1', '972.cx1', '1458.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 39916800, 443609999724, 39957619, 37885034880], 'label': '46656.ir.486.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713135
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1', '162.m1', '243.b1'], 'contains': ['972.ba1', '972.bb1', '972.bc1', '972.be1', '972.bh1', '972.bw1', '972.bx1', '972.cb1', '972.cd1', '972.cm1', '972.co1', '1458.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 499, 443130957804, 40320, 37885034880], 'label': '46656.ir.486.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713136
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.g1', '54.k1', '243.b1'], 'contains': ['972.bc1', '972.bg1', '972.bi1', '972.cc1', '972.ce1', '972.cn1', '972.cp1', '1458.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [443130957804, 37885034880, 39957619, 40320, 31658054844, 34136928000], 'label': '46656.ir.486.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713137
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1', '162.n1', '243.a1'], 'contains': ['972.bd1', '972.bm1', '972.bo1', '972.cl1', '972.da1', '972.do1', '972.dq1', '1458.i1', '1944.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [7, 655477406640, 39916800, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.486.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.h1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713138
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '12.i1', '12.q1', '12.bi1', '12.bo1', '12.bt1', '12.bw1'], 'contains': ['48.r1', '48.x1', '72.eq1', '72.ey1', '216.el1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 7, 41051299, 325, 269279866800, 1521641624], 'label': '46656.ir.24.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713139
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1', '54.m1', '243.a1'], 'contains': ['972.bd1', '972.db1', '972.dc1', '1458.j1', '1944.df1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 499, 39957564, 113215011840, 39916800, 2957880240], 'label': '46656.ir.486.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.i1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713140
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1', '54.n1', '243.a1'], 'contains': ['972.bd1', '972.dd1', '972.de1', '1458.k1', '1944.dg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 655477406640, 39916800, 6227827818, 2957880240, 31697930880], 'label': '46656.ir.486.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.j1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713141
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.h1', '54.o1', '243.b1'], 'contains': ['972.be1', '972.bf1', '972.bi1', '972.cq1', '972.cr1', '972.ct1', '972.cw1', '1458.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 499, 443609999724, 40320, 37885034880], 'label': '46656.ir.486.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713142
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.i1', '54.p1', '243.b1'], 'contains': ['972.bf1', '972.bg1', '972.bh1', '972.cs1', '972.cu1', '972.cv1', '972.cx1', '1458.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [37885034880, 39957619, 443609999724, 40320, 31658054844, 34136928000], 'label': '46656.ir.486.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713143
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.x1', '162.n1', '162.o1', '162.r1'], 'contains': ['972.j1', '972.k1', '972.l1', '972.m1', '972.t1', '972.u1', '972.v1', '972.y1', '972.bj1', '972.bk1', '972.bn1', '972.dk1', '972.dl1', '972.dm1', '972.dp1', '1458.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39957224, 39916800, 6227827207], 'label': '46656.ir.486.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '486.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.m1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713144
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.y1', '162.r1', '243.b1'], 'contains': ['972.n1', '972.o1', '972.w1', '972.z1', '972.bc1', '972.bf1', '972.bl1', '972.bq1', '972.bt1', '972.bu1', '972.bv1', '972.cf1', '972.df1', '972.dn1', '972.dr1', '1458.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 7, 39916800, 6227827207], 'label': '46656.ir.486.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.n1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713145
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.r1', '162.x1', '243.b1'], 'contains': ['972.f1', '972.g1', '972.p1', '972.q1', '972.be1', '972.bg1', '972.br1', '972.bs1', '972.bt1', '972.dg1', '972.dh1', '1458.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31697931324, 39957120, 41050800, 499, 39916800, 37885034880], 'label': '46656.ir.486.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713146
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.s1', '54.ba1', '243.b1'], 'contains': ['972.r1', '972.s1', '972.bh1', '972.bi1', '972.bt1', '972.di1', '972.dj1', '1458.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 39957120, 41050800, 39916800, 6227827818], 'label': '46656.ir.486.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.p1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713147
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bb1', '54.bf1', '243.b1'], 'contains': ['972.cb1', '972.ce1', '972.cf1', '972.cr1', '972.cx1', '972.dg1', '972.di1', '1458.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [34136928000, 31697931324, 39957120, 499, 443609999724, 37885034880], 'label': '46656.ir.486.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713245
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1', '216.bl1', '324.bi1', '324.bl1', '324.bo1'], 'contains': ['1296.bn1', '1296.di1', '1296.dm1', '1944.j1', '1944.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 268280812800, 39916800, 6227827818], 'label': '46656.ir.648.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713148
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bc1', '54.bg1', '243.b1'], 'contains': ['972.cc1', '972.cd1', '972.cf1', '972.cv1', '972.cw1', '972.dh1', '972.dj1', '1458.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [34136928000, 39917299, 31697931324, 39957120, 443609999724, 37885034880], 'label': '46656.ir.486.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713149
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '12.s1', '12.bg1', '12.bl1', '12.bt1', '12.bv1', '12.bz1'], 'contains': ['48.r1', '48.y1', '72.em1', '72.ez1', '216.em1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267744618, 7, 269279866800], 'label': '46656.ir.24.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713150
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1', '54.bh1', '243.a1'], 'contains': ['972.cl1', '972.db1', '972.dd1', '1458.l1', '1944.dc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [43673374524, 37924992444, 499, 536532640560, 37924992000, 2957880240], 'label': '46656.ir.486.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.s1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713151
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1', '54.bi1', '243.a1'], 'contains': ['972.cl1', '972.dc1', '972.de1', '1458.m1', '1944.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [43673374524, 37924992444, 39917299, 536532640560, 37924992000, 2957880240], 'label': '46656.ir.486.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.t1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713152
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1', '54.bj1', '243.a1'], 'contains': ['972.da1', '972.db1', '972.de1', '1458.n1', '1944.fb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 1174457, 39957120, 41050800, 7, 93576273840], 'label': '46656.ir.486.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.u1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713153
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.t1', '54.bk1', '243.a1'], 'contains': ['972.da1', '972.dc1', '972.dd1', '1458.o1', '1944.fc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 7, 93576273840, 6267668542], 'label': '46656.ir.486.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.v1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713154
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bd1', '54.bl1', '243.b1'], 'contains': ['972.cm1', '972.cp1', '972.cq1', '972.cu1', '972.df1', '972.dg1', '972.dj1', '1458.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 39957120, 41050800, 7, 355459144457], 'label': '46656.ir.486.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.w1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713155
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '486.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.be1', '54.bm1', '243.b1'], 'contains': ['972.cn1', '972.co1', '972.cs1', '972.ct1', '972.df1', '972.dh1', '972.di1', '1458.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 39957120, 41050800, 7, 274508640142], 'label': '46656.ir.486.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '486.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.x1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713156
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.a1', '288.b1', '288.q1', '288.bs1', '288.ch1', '288.ct1', '288.de1', '288.dl1'], 'contains': ['1728.b1', '1728.c1', '1728.d1', '1728.g1', '1728.h1', '1728.n1', '1728.o1', '1728.u1', '1728.v1', '1728.v2', '1728.bc1', '1728.bh1', '1728.bh2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [325, 1481684504, 269279866800, 37885034880], 'label': '46656.ir.576.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '576.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713157
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.a1', '288.c1', '288.r1', '288.bm1', '288.cc1', '288.cu1', '288.df1', '288.dm1'], 'contains': ['1728.c1', '1728.d1', '1728.e1', '1728.m1', '1728.o1', '1728.v1', '1728.v2', '1728.w1', '1728.bh1', '1728.bh2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40323593624, 268280812800, 39366316405, 37885034880], 'label': '46656.ir.576.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '576.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 216713158
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.a1', '192.b1', '192.c1', '288.d1', '288.h1', '288.s1', '288.bh1', '288.bn1', '288.bt1', '288.cd1', '288.ci1', '288.cv1', '288.dg1', '288.dn1'], 'contains': ['1728.a1', '1728.b1', '1728.e1', '1728.f1', '1728.u1', '1728.w1', '1728.x1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.576.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '576.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
  • id: 216713159
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.a1', '192.d1', '192.e1', '288.t1', '288.dh1', '288.do1'], 'contains': ['1728.f1', '1728.g1', '1728.m1', '1728.n1', '1728.o1', '1728.x1', '1728.bc1', '1728.bh1', '1728.bh2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [1481684725, 39366316080, 2917600664, 269279866800], 'label': '46656.ir.576.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '576.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713160
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.r1', '12.bh1', '12.bo1', '12.bp1', '12.bu1', '12.bz1'], 'contains': ['48.r1', '48.cl1', '72.fa1', '216.en1', '216.hb1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6227464938, 7, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.24.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713161
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.b1', '192.d1', '192.f1', '288.i1', '288.y1', '288.bc1', '288.bu1', '288.cm1', '288.cz1', '288.dp1'], 'contains': ['1728.f1', '1728.i1', '1728.y1', '1728.z1', '1728.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [40323593624, 132379435521, 40323593520, 269279866800], 'label': '46656.ir.576.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '576.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216713162
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.c1', '192.e1', '192.f1', '288.bd1', '288.cn1', '288.dq1'], 'contains': ['1728.f1', '1728.j1', '1728.z1', '1728.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [39366316080, 722937560115, 269279866800, 104], 'label': '46656.ir.576.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1', 'old_label': '576.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713163
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.b1', '192.e1', '192.g1', '288.j1', '288.bv1', '288.dr1'], 'contains': ['1728.f1', '1728.k1', '1728.ba1', '1728.bb1', '1728.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [39366316080, 622713012218, 325, 270715782960], 'label': '46656.ir.576.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.d1', 'old_label': '576.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.g1', 'subgroup_fusion': None, 'weyl_group': '108.28'}
  • id: 216713164
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.c1', '192.d1', '192.e1', '192.g1', '288.ds1'], 'contains': ['1728.f1', '1728.l1', '1728.bb1', '1728.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [193724576988, 325, 40323593520, 269279866800], 'label': '46656.ir.576.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '576.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.h1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216713165
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.f1', '288.bw1', '288.co1', '288.da1'], 'contains': ['1728.h1', '1728.i1', '1728.j1', '1728.bd1', '1728.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [40323593624, 387037284805, 300933848880, 461482882830], 'label': '46656.ir.576.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.ci1', 'old_label': '576.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713166
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.g1', '288.bx1'], 'contains': ['1728.h1', '1728.k1', '1728.l1', '1728.bf1', '1728.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [40323593624, 293708217925, 300933848880, 176887030590], 'label': '46656.ir.576.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.r1', 'old_label': '576.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.j1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 216713167
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '288.e1', '288.k1', '288.p1', '288.u1', '288.be1', '288.bk1', '288.bp1', '288.by1', '288.cf1', '288.cj1', '288.cp1', '288.cw1', '288.di1', '288.dt1', '288.eb1'], 'contains': ['1728.b1', '1728.c1', '1728.g1', '1728.m1', '1728.q1', '1728.r1', '1728.s1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [325, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.576.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '576.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.k1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216713168
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '288.a1', '288.f1', '288.l1', '288.v1', '288.bf1', '288.bl1', '288.bo1', '288.bq1', '288.ce1', '288.cg1', '288.cq1', '288.cx1', '288.cy1', '288.dj1', '288.du1'], 'contains': ['1728.d1', '1728.e1', '1728.n1', '1728.q1', '1728.s1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 325, 31658054504, 37885034880], 'label': '46656.ir.576.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '576.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.l1', 'subgroup_fusion': None, 'weyl_group': '32.25'}
  • id: 216713169
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1', '192.f1', '192.g1', '288.m1', '288.w1', '288.bg1', '288.br1', '288.cr1', '288.dk1', '288.dv1'], 'contains': ['1728.f1', '1728.h1', '1728.o1', '1728.r1', '1728.s1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 325, 269279866800, 104], 'label': '46656.ir.576.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '576.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.m1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216713170
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.f1', '288.n1', '288.x1', '288.bb1', '288.bz1', '288.cs1', '288.db1', '288.ec1'], 'contains': ['1728.i1', '1728.j1', '1728.p1', '1728.r1', '1728.t1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [300933848880, 325, 382729979624, 461482882830], 'label': '46656.ir.576.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '576.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.n1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216713171
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.s1', '12.bi1', '12.bn1', '12.bq1', '12.br1', '12.by1'], 'contains': ['48.r1', '48.cm1', '72.fb1', '216.eo1', '216.hc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6267381738, 269279866800], 'label': '46656.ir.24.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713172
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.g1', '288.o1', '288.ca1', '288.ed1'], 'contains': ['1728.k1', '1728.l1', '1728.r1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [300933848880, 325, 382729979624, 176887030590], 'label': '46656.ir.576.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '576.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.o1', 'subgroup_fusion': None, 'weyl_group': '24.9'}
  • id: 216713173
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ez1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '192.b1', '288.g1', '288.z1', '288.bi1', '288.cb1', '288.ck1', '288.dc1', '288.dw1'], 'contains': ['1728.a1', '1728.y1', '1728.ba1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.576.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '576.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.p1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713174
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gt1', '192.b1', '192.c1', '288.bj1', '288.cl1', '288.dx1'], 'contains': ['1728.a1', '1728.z1', '1728.bb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 463289990028], 'label': '46656.ir.576.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1', 'old_label': '576.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.q1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713175
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.b1', '192.d1', '288.ba1', '288.dd1', '288.dy1'], 'contains': ['1728.x1', '1728.y1', '1728.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [1481684725, 39366316080, 622713012218, 270715782960], 'label': '46656.ir.576.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '576.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.r1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713176
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.b1', '192.e1', '288.dz1'], 'contains': ['1728.x1', '1728.z1', '1728.ba1', '1728.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [624190336641, 40323593520, 269279866800, 31658054504], 'label': '46656.ir.576.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '576.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.s1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216713177
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.c1', '192.d1', '192.e1', '288.ea1'], 'contains': ['1728.x1', '1728.z1', '1728.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [40323593520, 269279866800, 34096648645, 463289990028], 'label': '46656.ir.576.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '576.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.t1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216713178
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '576.t2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['192.c1', '192.d1', '192.e1', '288.ea2'], 'contains': ['1728.x1', '1728.z1', '1728.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 128, 'diagramx': None, 'generators': [39366316080, 1481684504, 722937560115, 269279866800], 'label': '46656.ir.576.t2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '576.t2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.t2', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216713179
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1', '216.bh1', '324.a1', '324.b1', '324.c1'], 'contains': ['1296.b1', '1296.j1', '1296.w1', '1296.cq1', '1296.db1', '1296.gs1', '1296.kw1', '1944.a1', '1944.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 39916800, 6227827207], 'label': '46656.ir.648.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713180
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1', '216.bi1', '324.c1', '324.d1', '324.e1', '324.f1', '324.g1', '324.h1', '324.cp1'], 'contains': ['1296.b1', '1296.o1', '1296.bh1', '1296.cv1', '1296.cz1', '1296.ib1', '1296.ke1', '1944.c1', '1944.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 1134000, 37885034880], 'label': '46656.ir.648.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713181
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '216.bj1', '324.a1', '324.d1', '324.cc1'], 'contains': ['1296.b1', '1296.do1', '1296.dp1', '1944.e1', '1944.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 499, 1481684400, 39916800, 1481684844], 'label': '46656.ir.648.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216713182
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1', '12.d1', '12.bd1', '12.bl1'], 'contains': ['48.b1', '48.s1', '48.y1', '72.fd1', '72.fh1', '72.fl1', '72.fn1', '216.eq1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 499, 7, 325, 269279866800], 'label': '46656.ir.24.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216713183
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '216.bk1', '324.f1', '324.cc1', '324.cd1'], 'contains': ['1296.b1', '1296.dq1', '1296.dt1', '1944.f1', '1944.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1481684400, 269279866800, 40320, 39957619, 1481684844], 'label': '46656.ir.648.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713184
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1', '216.bl1', '324.a1', '324.b1', '324.g1'], 'contains': ['1296.b1', '1296.dr1', '1296.dv1', '1944.j1', '1944.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 1481684400, 39916800, 6227827818], 'label': '46656.ir.648.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713185
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1', '216.bm1', '324.b1', '324.d1', '324.cd1'], 'contains': ['1296.b1', '1296.ds1', '1296.du1', '1944.h1', '1944.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31658054844, 268280812800, 1134000, 39957619, 37885034880], 'label': '46656.ir.648.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713186
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.d1', '216.bn1', '324.i1'], 'contains': ['1296.d1', '1296.f1', '1296.v1', '1296.ei1', '1296.es1', '1296.fl1', '1296.ko1', '1944.a1', '1944.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39366316080, 7, 39916800, 6227827207, 435], 'label': '46656.ir.648.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713187
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.b1', '216.e1', '216.bo1', '324.i1'], 'contains': ['1296.d1', '1296.i1', '1296.y1', '1296.ej1', '1296.ev1', '1296.gt1', '1296.ky1', '1944.b1', '1944.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [7, 39916800, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.648.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '648.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713188
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.c1', '216.f1', '216.bq1', '324.ce1'], 'contains': ['1296.c1', '1296.m1', '1296.bb1', '1296.em1', '1296.eq1', '1296.hs1', '1296.jj1', '1944.c1', '1944.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39957120, 7, 31697931315, 1134000, 37885034880], 'label': '46656.ir.648.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '648.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713189
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.c1', '216.g1', '216.bp1', '324.i1'], 'contains': ['1296.d1', '1296.n1', '1296.bc1', '1296.eo1', '1296.er1', '1296.ht1', '1296.jk1', '1944.d1', '1944.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39957555, 387037284480, 39957120, 7, 1134000], 'label': '46656.ir.648.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713190
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1', '216.e1', '216.br1', '324.j1', '324.k1', '324.l1'], 'contains': ['1296.e1', '1296.h1', '1296.ba1', '1296.ex1', '1296.fa1', '1296.fq1', '1296.kp1', '1944.m1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7, 325, 39916800, 6227827207, 104], 'label': '46656.ir.648.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '648.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.k1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713191
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1', '216.g1', '216.bs1', '324.l1', '324.m1', '324.n1', '324.o1', '324.p1', '324.q1', '324.bu1'], 'contains': ['1296.e1', '1296.l1', '1296.bf1', '1296.ey1', '1296.ez1', '1296.ho1', '1296.in1', '1944.n1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 7, 325, 39957224, 1134000], 'label': '46656.ir.648.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.l1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713192
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1', '216.l1', '216.bt1', '324.j1', '324.m1', '324.z1'], 'contains': ['1296.a1', '1296.e1', '1296.fb1', '5832.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [499, 7, 325, 39916800, 104], 'label': '46656.ir.648.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.m1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713193
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.be1', '12.bm1'], 'contains': ['48.s1', '48.v1', '48.w1', '72.fe1', '72.fi1', '72.fo1', '216.er1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 7, 6227827818, 325, 269279866800], 'label': '46656.ir.24.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216713194
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1', '216.j1', '216.bu1', '324.o1', '324.z1', '324.ba1'], 'contains': ['1296.e1', '1296.fb1', '1296.fe1', '5832.d1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7, 39957619, 104, 40320, 325], 'label': '46656.ir.648.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '648.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713195
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.m1', '216.n1', '216.bv1', '324.j1', '324.k1', '324.p1'], 'contains': ['1296.e1', '1296.fc1', '1296.ff1', '5832.e1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7, 325, 39916800, 6227827818, 104], 'label': '46656.ir.648.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '648.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713196
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.k1', '216.o1', '216.bw1', '324.k1', '324.m1', '324.ba1'], 'contains': ['1296.e1', '1296.fd1', '1296.fe1', '5832.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [7, 325, 1134000, 39957619, 104], 'label': '46656.ir.648.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.p1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713197
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.p1', '216.q1', '216.bx1', '324.i1'], 'contains': ['1296.f1', '1296.y1', '1296.bc1', '1296.fu1', '1296.fz1', '1296.kq1', '1296.kt1', '1944.o1', '1944.p1', '1944.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1174327, 39916800, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.648.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713198
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.p1', '216.r1', '216.by1'], 'contains': ['1296.g1', '1296.z1', '1296.be1', '1296.fv1', '1296.gc1', '1296.kr1', '1296.ku1', '1944.o1', '1944.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1174327, 40323593845, 39916800, 6227827207, 104], 'label': '46656.ir.648.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.r1', 'old_label': '648.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713199
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.p1', '216.s1', '216.bz1', '324.l1'], 'contains': ['1296.h1', '1296.ba1', '1296.bf1', '1296.fw1', '1296.gd1', '1296.ks1', '1296.kv1', '1944.o1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 325, 39916800, 6227827207, 104], 'label': '46656.ir.648.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.s1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713200
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.t1', '216.ca1', '324.l1', '324.r1', '324.bv1'], 'contains': ['1296.h1', '1296.l1', '1296.fg1', '1296.gl1', '1296.ii1', '1944.r1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174320, 39916800, 6227827200, 104, 1174645], 'label': '46656.ir.648.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.t1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713201
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.q1', '216.r1', '216.s1', '216.cb1', '324.i1'], 'contains': ['1296.i1', '1296.v1', '1296.bc1', '1296.gx1', '1296.hd1', '1296.lc1', '1296.ln1', '1944.o1', '1944.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1174327, 39366316080, 39916800, 6227827207, 435], 'label': '46656.ir.648.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.u1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713202
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.q1', '216.cd1', '324.c1'], 'contains': ['1296.j1', '1296.w1', '1296.bh1', '1296.gy1', '1296.hf1', '1296.lf1', '1296.lo1', '1944.p1', '1944.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684400, 39916800, 6227827207], 'label': '46656.ir.648.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.v1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713203
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.q1', '216.r1', '216.cc1'], 'contains': ['1296.k1', '1296.x1', '1296.bi1', '1296.gz1', '1296.hi1', '1296.li1', '1296.lp1', '1944.q1', '1944.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684504, 39916800, 6227827207], 'label': '46656.ir.648.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '648.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.w1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713204
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1', '12.e1', '12.bd1', '12.bm1'], 'contains': ['48.c1', '48.s1', '48.w1', '72.ff1', '72.fj1', '72.fm1', '72.fp1', '216.es1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 6227389338, 1481684400, 7, 325, 269279866800], 'label': '46656.ir.24.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216713205
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.t1', '216.u1', '216.ce1', '324.i1'], 'contains': ['1296.f1', '1296.i1', '1296.n1', '1296.fj1', '1296.gn1', '1296.hk1', '1296.jh1', '1944.r1', '1944.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1174320, 39916800, 6227827200, 435], 'label': '46656.ir.648.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '648.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713206
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.u1', '216.cf1', '324.c1', '324.s1', '324.cq1'], 'contains': ['1296.j1', '1296.o1', '1296.gq1', '1296.hn1', '1296.kd1', '1944.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 39916800, 6227827200], 'label': '46656.ir.648.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.y1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713207
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.v1', '216.ch1', '324.r1', '324.t1', '324.bu1'], 'contains': ['1296.l1', '1296.u1', '1296.ho1', '1296.io1', '1296.it1', '1944.u1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050807, 39957120, 325, 39957224, 1134000], 'label': '46656.ir.648.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.z1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713208
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.w1', '216.ci1', '324.l1', '324.t1', '324.ca1'], 'contains': ['1296.l1', '1296.ba1', '1296.hr1', '1296.iq1', '1296.iw1', '1944.v1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174320, 39916800, 6227827207, 104, 1174645], 'label': '46656.ir.648.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ba1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713209
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1', '216.cj1', '324.n1', '324.t1', '324.bv1'], 'contains': ['1296.l1', '1296.jd1', '1296.je1', '1944.w1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 1174320, 39916800, 104, 1174645], 'label': '46656.ir.648.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bb1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713210
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1', '216.ck1', '324.n1', '324.r1', '324.ca1'], 'contains': ['1296.l1', '1296.jf1', '1296.jg1', '1944.x1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381127, 1174320, 39916800, 104, 1174645], 'label': '46656.ir.648.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bc1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713211
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.v1', '216.x1', '216.cl1', '324.ce1'], 'contains': ['1296.m1', '1296.p1', '1296.s1', '1296.hs1', '1296.hu1', '1296.jq1', '1296.jt1', '1944.u1', '1944.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41050807, 39957120, 31697931315, 1134000, 37885034880], 'label': '46656.ir.648.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '648.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713212
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.w1', '216.y1', '216.cm1', '324.i1'], 'contains': ['1296.n1', '1296.v1', '1296.y1', '1296.hx1', '1296.ia1', '1296.js1', '1296.jw1', '1944.v1', '1944.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39366316080, 1174320, 39916800, 6227827207, 435], 'label': '46656.ir.648.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.be1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713213
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.x1', '216.cn1', '324.s1', '324.u1', '324.cp1'], 'contains': ['1296.o1', '1296.r1', '1296.id1', '1296.kf1', '1296.kh1', '1944.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 1134000, 37885034880], 'label': '46656.ir.648.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bf1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713214
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.y1', '216.co1', '324.c1', '324.u1', '324.cr1'], 'contains': ['1296.o1', '1296.w1', '1296.ig1', '1296.kg1', '1296.ki1', '1944.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 39916800, 6227827207], 'label': '46656.ir.648.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bg1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713215
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.j1', '4.k1', '6.j1', '6.k1', '8.h1', '54.l1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.2.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.j1', '4.k1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216713216
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['11664.l1', '11664.o1', '11664.p1', '11664.m1', '11664.n1', '11664.bn1', '11664.bm1', '11664.q1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.d1', '8.e1', '8.f1', '12.cc1', '12.cd1', '16.l1', '108.fk1'], 'core': '4.k1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 41051125, 39916807, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.4.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.d1', '8.e1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '46656.ir', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216713217
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '12.be1', '12.bl1'], 'contains': ['48.s1', '48.x1', '48.y1', '72.fg1', '72.fk1', '72.fq1', '216.et1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1174819, 1481684400, 7, 325, 269279866800], 'label': '46656.ir.24.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216713218
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.z1', '216.cp1', '324.e1', '324.u1', '324.cq1'], 'contains': ['1296.o1', '1296.kj1', '1296.kk1', '5832.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 39916800], 'label': '46656.ir.648.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bh1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713219
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ba1', '216.cq1', '324.e1', '324.s1', '324.cr1'], 'contains': ['1296.o1', '1296.kl1', '1296.km1', '5832.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 39916800], 'label': '46656.ir.648.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bi1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713220
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '216.cr1', '324.q1'], 'contains': ['1296.bf1', '1296.lu1', '1296.lv1', '5832.m1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 6267669018, 325, 39916800, 104], 'label': '46656.ir.648.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.g1', 'old_label': '648.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bj1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713221
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1', '216.ct1', '324.h1'], 'contains': ['1296.bh1', '1296.lw1', '1296.lx1', '5832.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 6267669018, 1481684400, 1174789, 39916800], 'label': '46656.ir.648.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bk1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713222
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.p1', '216.cs1'], 'contains': ['1296.bj2', '1296.ly1', '1296.lz1', '5832.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267669018, 33138564487, 37885034984, 39916800, 33139371205], 'label': '46656.ir.648.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.bl1', 'old_label': '648.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bl1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713223
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bb1', '216.cu1', '324.v1', '324.w1', '324.ce1'], 'contains': ['1296.c1', '1296.p1', '1296.bk1', '1296.ep1', '1296.ik1', '1944.ba1', '1944.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1521641955, 39957120, 7, 1481684400, 39916800], 'label': '46656.ir.648.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713224
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bb1', '216.cv1', '324.x1', '324.y1', '324.z1', '324.ba1', '324.bb1', '324.bc1', '324.bu1'], 'contains': ['1296.e1', '1296.u1', '1296.bm1', '1296.ez1', '1296.io1', '1944.bb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 7, 325, 39957224, 39916800], 'label': '46656.ir.648.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bn1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713225
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bv1', '216.bc1', '324.v1', '324.bd1', '324.cf1'], 'contains': ['1296.bk1', '1296.gj1', '1296.ix1', '1944.bc1', '1944.bd1', '1944.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [355419187635, 268280812800, 1174320, 6227827200, 40320], 'label': '46656.ir.648.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '648.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bo1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 216713226
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bu1', '216.bc1', '324.be1'], 'contains': ['1296.bl1', '1296.gk1', '1296.jb1', '1944.bc1', '1944.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268281987445, 1174320, 6227827200, 355419187304, 40320], 'label': '46656.ir.648.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '648.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713227
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bw1', '216.bc1', '324.x1', '324.bf1', '324.bv1'], 'contains': ['1296.bm1', '1296.gl1', '1296.jd1', '1944.bc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174320, 6227827200, 40320, 104, 1174645], 'label': '46656.ir.648.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bq1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216713228
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1', '12.bk1'], 'contains': ['48.t1', '48.z1', '48.bc1', '72.fl1', '72.fr1', '216.eu1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267744007, 39366316080, 499, 7, 325, 270715782960, 104, 716634334350], 'label': '46656.ir.24.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '24.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216713229
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bx1', '216.bd1', '324.y1', '324.bg1', '324.bv1'], 'contains': ['1296.bm1', '1296.ii1', '1296.je1', '1944.bf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 1174320, 40320, 104, 1174645], 'label': '46656.ir.648.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.br1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216713230
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.by1', '216.bd1', '324.w1', '324.bh1', '324.cf1'], 'contains': ['1296.bk1', '1296.ij1', '1296.iy1', '1944.bf1', '1944.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267381120, 355419187635, 268280812800, 1174320, 40320], 'label': '46656.ir.648.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '648.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bs1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216713231
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.be1', '216.cx1', '324.bd1', '324.bh1', '324.ce1'], 'contains': ['1296.s1', '1296.bb1', '1296.bk1', '1296.il1', '1296.ir1', '1944.bh1', '1944.bi1', '1944.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41050807, 1521641955, 39957120, 1481684400, 39916800], 'label': '46656.ir.648.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713232
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.be1', '216.cw1', '324.be1'], 'contains': ['1296.t1', '1296.bd1', '1296.bl1', '1296.im1', '1296.is1', '1944.bh1', '1944.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41050807, 39957120, 325, 39916800, 1521641624], 'label': '46656.ir.648.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '648.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bu1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713233
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.be1', '216.cy1', '324.bf1', '324.bg1', '324.bu1'], 'contains': ['1296.u1', '1296.bf1', '1296.bm1', '1296.in1', '1296.it1', '1944.bh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050807, 39957120, 325, 39957224, 39916800], 'label': '46656.ir.648.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bv1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713234
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cc1', '216.bf1', '324.v1', '324.bh1', '324.cg1'], 'contains': ['1296.bk1', '1296.ip1', '1296.iz1', '1944.bk1', '1944.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 1174320, 355419187304, 40320, 6227827207], 'label': '46656.ir.648.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216713235
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cd1', '216.bf1', '324.x1', '324.bg1', '324.ca1'], 'contains': ['1296.bm1', '1296.iq1', '1296.jf1', '1944.bl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 104, 40320], 'label': '46656.ir.648.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bx1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713236
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cf1', '216.bg1', '324.w1', '324.bd1', '324.cg1'], 'contains': ['1296.bk1', '1296.iu1', '1296.ja1', '1944.bm1', '1944.bn1', '1944.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 6267381127, 268280812800, 1174320, 40320], 'label': '46656.ir.648.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.by1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713237
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ce1', '216.bg1', '324.be1'], 'contains': ['1296.bl1', '1296.iv1', '1296.jc1', '1944.bm1', '1944.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267381127, 1174320, 268280812904, 40320, 1174645], 'label': '46656.ir.648.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '648.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.bz1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 216713238
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cg1', '216.bg1', '324.y1', '324.bf1', '324.ca1'], 'contains': ['1296.bm1', '1296.iw1', '1296.jg1', '1944.bm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381127, 1174320, 40320, 104, 1174645], 'label': '46656.ir.648.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ca1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713239
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1', '12.bk1'], 'contains': ['48.t1', '48.ba1', '48.bb1', '72.fm1', '72.fs1', '216.ev1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 6227389338, 270715782960, 104, 716634334350], 'label': '46656.ir.24.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '24.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216713240
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bh1', '216.bn1', '324.bi1', '324.bj1', '324.bm1'], 'contains': ['1296.bn1', '1296.br1', '1296.cb1', '1296.co1', '1296.da1', '1296.fm1', '1296.kx1', '1944.a1', '1944.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 39916800, 6227827207], 'label': '46656.ir.648.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713241
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bh1', '216.bo1', '324.bk1', '324.bl1', '324.bm1'], 'contains': ['1296.bn1', '1296.bt1', '1296.cd1', '1296.cp1', '1296.dd1', '1296.gu1', '1296.lq1', '1944.b1', '1944.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 7, 39916800, 40323593520, 6227827207], 'label': '46656.ir.648.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713242
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bi1', '216.bp1', '324.bm1', '324.bn1', '324.bo1'], 'contains': ['1296.bn1', '1296.bv1', '1296.cg1', '1296.cu1', '1296.cx1', '1296.ic1', '1296.jl1', '1944.d1', '1944.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 39957120, 7, 1481684400, 1134000], 'label': '46656.ir.648.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713243
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bi1', '216.bq1', '324.bp1', '324.bq1', '324.cp1'], 'contains': ['1296.bo1', '1296.bw1', '1296.cj1', '1296.cv1', '1296.cy1', '1296.id1', '1296.jn1', '1944.c1', '1944.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 1134000], 'label': '46656.ir.648.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ce1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713244
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1', '216.bj1', '324.bi1', '324.bk1', '324.bn1'], 'contains': ['1296.bn1', '1296.dg1', '1296.dh1', '1944.i1', '1944.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 268280812800, 499, 444, 39916800], 'label': '46656.ir.648.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713246
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1', '216.bl1', '324.bj1', '324.bk1', '324.bo1'], 'contains': ['1296.bn1', '1296.dj1', '1296.dn1', '1944.k1', '1944.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 268280812800, 39916800, 6227827818, 40323593520], 'label': '46656.ir.648.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ch1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713247
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1', '216.bm1', '324.bj1', '324.bl1', '324.bn1'], 'contains': ['1296.bn1', '1296.dk1', '1296.dl1', '1944.l1', '1944.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 1481684400, 1134000, 39957619, 1481684844], 'label': '46656.ir.648.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ci1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713248
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1', '216.bj1', '324.bp1', '324.cc1', '324.cj1'], 'contains': ['1296.bo1', '1296.do1', '1296.dq1', '1944.e1', '1944.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [31658054844, 268280812800, 499, 39916800, 37885034880], 'label': '46656.ir.648.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '648.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713249
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '216.bk1', '324.bq1', '324.cc1', '324.ck1'], 'contains': ['1296.bo1', '1296.dp1', '1296.dt1', '1944.f1', '1944.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 40320, 39957619, 1481684844], 'label': '46656.ir.648.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713250
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1'], 'contains': ['48.u1', '48.bd1', '48.be1', '72.fl1', '72.ft1', '216.ew1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6267744007, 39366316080, 455255499150, 499, 7, 325, 270715782960, 104], 'label': '46656.ir.24.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '24.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216713251
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1', '216.bk1', '324.bq1', '324.cd1', '324.cj1'], 'contains': ['1296.bo1', '1296.dq1', '1296.du1', '1944.g1', '1944.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [31658054844, 268280812800, 40320, 39957619, 37885034880], 'label': '46656.ir.648.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '648.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713252
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bd1', '216.bm1', '324.bp1', '324.cd1', '324.ck1'], 'contains': ['1296.bo1', '1296.ds1', '1296.dt1', '1944.h1', '1944.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 1134000, 39957619, 1481684844], 'label': '46656.ir.648.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713253
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bn1', '216.bo1', '216.br1', '324.br1'], 'contains': ['1296.bp1', '1296.bq1', '1296.cc1', '1296.eg1', '1296.et1', '1296.fo1', '1296.kz1', '1944.m1', '1944.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268280812800, 7, 39916800, 355419187304, 6227827207], 'label': '46656.ir.648.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '648.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713254
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bp1', '216.bq1', '216.bs1', '324.br1', '324.bt1', '324.ce1'], 'contains': ['1296.bp1', '1296.bu1', '1296.cf1', '1296.em1', '1296.ep1', '1296.hu1', '1296.il1', '1944.n1', '1944.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1521641955, 39957120, 7, 1481684400, 1134000], 'label': '46656.ir.648.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.co1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713255
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bx1', '216.by1', '216.bz1', '216.cb1', '324.br1'], 'contains': ['1296.bq1', '1296.cc1', '1296.cf1', '1296.fr1', '1296.fx1', '1296.la1', '1296.lk1', '1944.o1', '1944.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [355419187635, 1174327, 268280812800, 39916800, 6227827207], 'label': '46656.ir.648.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '648.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713256
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bx1', '216.cd1', '324.bm1'], 'contains': ['1296.br1', '1296.cd1', '1296.cg1', '1296.fs1', '1296.ge1', '1296.ld1', '1296.ll1', '1944.p1', '1944.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 268280812800, 39916800, 40323593520, 6227827207], 'label': '46656.ir.648.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713257
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.bx1', '216.by1', '216.cc1'], 'contains': ['1296.bs1', '1296.ce1', '1296.ci1', '1296.ft1', '1296.gf1', '1296.le1', '1296.lm1', '1944.q1', '1944.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1174327, 268280812800, 39916800, 40323593955, 6227827207], 'label': '46656.ir.648.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '648.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713258
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ca1', '216.ce1', '324.br1', '324.bw1', '324.cf1'], 'contains': ['1296.bq1', '1296.bu1', '1296.fh1', '1296.gj1', '1296.ij1', '1944.r1', '1944.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 6227827200, 355419187304], 'label': '46656.ir.648.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '648.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713259
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cb1', '216.cc1', '216.cd1', '324.bm1'], 'contains': ['1296.bt1', '1296.cb1', '1296.cg1', '1296.gw1', '1296.he1', '1296.lr1', '1296.lt1', '1944.s1', '1944.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 39366316080, 268280812800, 39916800, 6227827207], 'label': '46656.ir.648.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ct1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713260
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ha1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ce1', '216.cf1', '324.bm1'], 'contains': ['1296.br1', '1296.bt1', '1296.bv1', '1296.fk1', '1296.gp1', '1296.hl1', '1296.ji1', '1944.t1', '1944.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 39916800, 6227827200], 'label': '46656.ir.648.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '648.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713261
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1'], 'contains': ['48.bf1', '48.bg1', '48.bh1', '48.bq1', '48.bt1', '48.cg1', '48.cj1', '72.fu1', '72.fv1', '72.fw1', '72.fx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.24.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216713262
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.x1', '216.cg1', '324.bs1', '324.bx1', '324.by1'], 'contains': ['1296.jz1', '1944.bx1', '1944.by1', '1944.bz1', '2592.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 39957224, 39916800, 132379435521, 1520467200], 'label': '46656.ir.648.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '648.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216713263
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.y1', '216.cg1', '324.bz1'], 'contains': ['1296.ka1', '1944.bx1', '1944.bz1', '2592.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [2957880565, 37924992000, 39916800, 2957880240, 463289990028], 'label': '46656.ir.648.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bq1', 'old_label': '648.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713264
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cg1', '216.cz1', '324.bu1', '324.bv1', '324.ca1'], 'contains': ['1296.l1', '1296.bm1', '1296.kb1', '1944.bx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 39916800], 'label': '46656.ir.648.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '648.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cx1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713265
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ch1', '216.cl1', '324.bw1', '324.cb1', '324.ce1'], 'contains': ['1296.bu1', '1296.by1', '1296.hs1', '1296.ik1', '1296.ir1', '1944.u1', '1944.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41050807, 1521641955, 39957120, 1481684400, 1134000], 'label': '46656.ir.648.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713266
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ci1', '216.cm1', '324.br1', '324.cb1', '324.cg1'], 'contains': ['1296.bu1', '1296.cc1', '1296.hv1', '1296.ip1', '1296.iu1', '1944.v1', '1944.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 355419187304, 6227827207], 'label': '46656.ir.648.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.cz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713267
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bo1', '216.cj1', '324.bt1', '324.cb1', '324.cf1'], 'contains': ['1296.bu1', '1296.ix1', '1296.iy1', '1944.w1', '1944.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267381120, 355419187635, 268280812800, 1174320, 39916800], 'label': '46656.ir.648.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '648.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.da1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713268
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.bp1', '216.ck1', '324.bt1', '324.bw1', '324.cg1'], 'contains': ['1296.bu1', '1296.iz1', '1296.ja1', '1944.x1', '1944.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 39916800, 355419187304], 'label': '46656.ir.648.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.db1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713269
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cl1', '216.cn1', '324.cp1'], 'contains': ['1296.bw1', '1296.bx1', '1296.ca1', '1296.ib1', '1296.id1', '1296.jp1', '1296.jv1', '1944.y1', '1944.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 1481684400, 1134000], 'label': '46656.ir.648.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713270
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cm1', '216.co1', '324.bm1'], 'contains': ['1296.bv1', '1296.cb1', '1296.cd1', '1296.ie1', '1296.if1', '1296.jr1', '1296.jx1', '1944.z1', '1944.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 39916800, 6227827207], 'label': '46656.ir.648.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713271
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cu1', '216.da1', '324.cc1', '324.cd1', '324.cp1'], 'contains': ['1296.b1', '1296.r1', '1296.bo1', '1296.bx1', '1296.cm1', '1296.cy1', '1296.jp1', '1944.ba1', '1944.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 39916800], 'label': '46656.ir.648.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713272
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.t1', '12.ca1'], 'contains': ['48.bg1', '48.bi1', '48.bj1', '48.bv1', '48.bz1', '72.fy1', '72.fz1', '72.ga1', '72.gb1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827200, 1174645], 'label': '46656.ir.24.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713273
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cu1', '216.cv1', '216.db1', '324.ce1'], 'contains': ['1296.c1', '1296.s1', '1296.bp1', '1296.by1', '1296.ck1', '1296.eq1', '1296.jq1', '1944.bb1', '1944.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39957120, 7, 31697931315, 39916800, 37885034880], 'label': '46656.ir.648.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '648.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.df1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713274
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cw1', '216.cx1', '216.cy1', '216.dh1', '324.ce1'], 'contains': ['1296.p1', '1296.bb1', '1296.by1', '1296.cf1', '1296.ck1', '1296.jj1', '1296.jt1', '1944.bh1', '1944.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41050807, 39957120, 39916800, 31697930984, 37885034880], 'label': '46656.ir.648.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '648.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713275
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cw1', '216.cx1', '216.di1'], 'contains': ['1296.q1', '1296.bg1', '1296.bz1', '1296.ch1', '1296.cl1', '1296.jm1', '1296.ju1', '1944.bj1', '1944.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [41050807, 39957120, 39916800, 37885034880, 1521641624], 'label': '46656.ir.648.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '648.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713276
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cx1', '216.dj1', '324.cp1'], 'contains': ['1296.r1', '1296.bh1', '1296.ca1', '1296.cj1', '1296.cm1', '1296.jn1', '1296.jv1', '1944.bi1', '1944.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 1481684400, 39916800], 'label': '46656.ir.648.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.di1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713277
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.cz1', '216.dp1', '324.ce1', '324.cf1', '324.cg1'], 'contains': ['1296.m1', '1296.bk1', '1296.bu1', '1296.ck1', '1296.kc1', '1944.bx1', '1944.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 41050800, 31697931315, 39916800, 37885034880], 'label': '46656.ir.648.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '648.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713278
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.da1', '216.db1', '324.ch1', '324.ci1', '324.cj1', '324.ck1', '324.cl1', '324.cm1', '324.cp1'], 'contains': ['1296.bo1', '1296.ca1', '1296.cn1', '1296.cz1', '1296.kf1', '1944.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 39916800, 37885034880], 'label': '46656.ir.648.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dk1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713279
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dc1', '216.dd1', '216.de1', '324.ch1', '324.cn1', '324.cq1'], 'contains': ['1296.cn1', '1296.hn1', '1296.kj1', '5832.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227827200, 40320], 'label': '46656.ir.648.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '648.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dl1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713280
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.df1', '216.dg1', '324.ci1', '324.co1', '324.cq1'], 'contains': ['1296.cn1', '1296.kd1', '1296.kk1', '5832.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 40320], 'label': '46656.ir.648.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dm1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713281
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dh1', '216.di1', '216.dj1', '324.cn1', '324.co1', '324.cp1'], 'contains': ['1296.bx1', '1296.cj1', '1296.cn1', '1296.ke1', '1296.kh1', '1944.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 39916800, 37885034880], 'label': '46656.ir.648.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713282
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dk1', '216.dl1', '324.ch1', '324.co1', '324.cr1'], 'contains': ['1296.cn1', '1296.kg1', '1296.kl1', '5832.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 40320, 6227827207], 'label': '46656.ir.648.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.do1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713283
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.n1', '12.ca1'], 'contains': ['48.bj1', '48.bw1', '48.cc1', '72.gc1', '72.gd1', '216.ih1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40327, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827200, 1174645], 'label': '46656.ir.24.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713284
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dm1', '216.dn1', '216.do1', '324.ci1', '324.cn1', '324.cr1'], 'contains': ['1296.cn1', '1296.ki1', '1296.km1', '5832.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 40320], 'label': '46656.ir.648.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dp1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713285
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.dp1', '324.cp1', '324.cq1', '324.cr1'], 'contains': ['1296.o1', '1296.bw1', '1296.cm1', '1296.cn1', '1296.kn1', '1944.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 39916800, 37885034880], 'label': '46656.ir.648.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dq1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713286
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dq1', '216.ex1', '324.bm1', '324.cs1', '324.ct1'], 'contains': ['1296.co1', '1296.cu1', '1296.dd1', '1296.fk1', '1296.ge1', '1296.ie1', '1296.lr1', '1944.ci1', '1944.cj1', '1944.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 7, 6227827207], 'label': '46656.ir.648.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713287
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1', '216.dr1', '324.bi1', '324.cs1', '324.da1'], 'contains': ['1296.co1', '1296.dg1', '1296.di1', '1944.cl1', '1944.cp1', '1944.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 499, 443130957804, 270715782960, 37885034880], 'label': '46656.ir.648.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ds1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713288
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.db1', '216.ds1', '324.bi1', '324.ct1', '324.db1'], 'contains': ['1296.co1', '1296.dh1', '1296.dm1', '1944.cm1', '1944.cs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 40819, 443130957804, 270715782960, 37885034880], 'label': '46656.ir.648.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713289
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dc1', '216.dt1', '324.bj1', '324.ct1', '324.da1'], 'contains': ['1296.co1', '1296.dj1', '1296.dl1', '1944.cn1', '1944.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41051299, 270715782960, 742619410284, 37885034880], 'label': '46656.ir.648.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.du1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713290
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dd1', '216.du1', '324.bj1', '324.cs1', '324.db1'], 'contains': ['1296.co1', '1296.dk1', '1296.dn1', '1944.co1', '1944.cq1', '1944.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091619, 270715782960, 742619410284, 37885034880], 'label': '46656.ir.648.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713291
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dw1', '216.ey1', '324.cu1'], 'contains': ['1296.cs1', '1296.ct1', '1296.de1', '1296.go1', '1296.hb1', '1296.hy1', '1296.ls1', '1944.cj1', '1944.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 300933848880, 7, 6227827207, 93575951280], 'label': '46656.ir.648.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '648.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713292
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dq1', '216.ez1', '324.bm1', '324.cv1', '324.cw1'], 'contains': ['1296.cp1', '1296.cu1', '1296.da1', '1296.gp1', '1296.he1', '1296.if1', '1296.ld1', '1944.ci1', '1944.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 40323593520, 6227827207], 'label': '46656.ir.648.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713293
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dq1', '216.fa1', '324.c1', '324.cx1', '324.cy1'], 'contains': ['1296.cq1', '1296.cv1', '1296.db1', '1296.gq1', '1296.hf1', '1296.ig1', '1296.lf1', '1944.ck1', '1944.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 1481684400, 6227827207], 'label': '46656.ir.648.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713294
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.t1', '12.bj1'], 'contains': ['48.bj1', '48.by1', '48.cd1', '72.ge1', '72.gf1', '72.gg1', '216.ij1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 269279866800, 39957127, 1174645], 'label': '46656.ir.24.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713295
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dq1', '216.dw1', '216.fb1', '324.cz1'], 'contains': ['1296.cr1', '1296.cw1', '1296.dc1', '1296.gr1', '1296.hg1', '1296.ih1', '1296.lg1', '1944.cj1', '1944.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 7, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.648.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '648.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.dz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713296
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.di1', '216.dr1', '324.bk1', '324.cv1', '324.da1'], 'contains': ['1296.cp1', '1296.dg1', '1296.dj1', '1944.cl1', '1944.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [31658054844, 499, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.648.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ea1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713297
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dj1', '216.ds1', '324.bk1', '324.cw1', '324.db1'], 'contains': ['1296.cp1', '1296.dh1', '1296.dn1', '1944.cm1', '1944.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [31658054844, 40819, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.648.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713298
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dk1', '216.dt1', '324.bl1', '324.cw1', '324.da1'], 'contains': ['1296.cp1', '1296.di1', '1296.dl1', '1944.cn1', '1944.da1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41051299, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.648.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ec1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713299
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dl1', '216.du1', '324.bl1', '324.cv1', '324.db1'], 'contains': ['1296.cp1', '1296.dk1', '1296.dm1', '1944.co1', '1944.db1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091619, 443130957804, 269279866800, 37885034880], 'label': '46656.ir.648.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ed1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713300
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dm1', '216.dr1', '324.a1', '324.cx1', '324.dc1'], 'contains': ['1296.cq1', '1296.do1', '1296.dr1', '1944.cr1', '1944.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [499, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.648.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ee1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713301
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dn1', '216.ds1', '324.a1', '324.cy1', '324.dd1'], 'contains': ['1296.cq1', '1296.dp1', '1296.dv1', '1944.cs1', '1944.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [40819, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.648.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ef1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713302
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.do1', '216.dt1', '324.b1', '324.cy1', '324.dc1'], 'contains': ['1296.cq1', '1296.dr1', '1296.du1', '1944.ct1', '1944.da1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41051299, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.648.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713303
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dp1', '216.du1', '324.b1', '324.cx1', '324.dd1'], 'contains': ['1296.cq1', '1296.ds1', '1296.dv1', '1944.cu1', '1944.db1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091619, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.648.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713304
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dq1', '216.dr1', '216.dx1', '324.cz1'], 'contains': ['1296.cr1', '1296.dw1', '1296.dx1', '1944.cp1', '1944.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 499, 443130957804, 444, 269279866800], 'label': '46656.ir.648.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '648.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ei1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713305
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '12.w1', '12.bj1', '12.ca1'], 'contains': ['48.d1', '48.bj1', '48.cb1', '72.gh1', '72.gi1', '216.ik1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 6227827200, 1521641624], 'label': '46656.ir.24.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216713306
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dr1', '216.du1', '216.dy1', '324.cz1'], 'contains': ['1296.cr1', '1296.dy1', '1296.dz1', '1944.cq1', '1944.db1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091619, 39366316080, 443130957804, 444, 269279866800], 'label': '46656.ir.648.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '648.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ej1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713307
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ds1', '216.dx1', '324.cu1'], 'contains': ['1296.cs1', '1296.ea1', '1296.eb1', '1944.cp1', '1944.dc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [301891126320, 499, 655477406640, 444, 6227389164], 'label': '46656.ir.648.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '648.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ek1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713308
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dt1', '216.dy1', '324.cu1'], 'contains': ['1296.cs1', '1296.ec1', '1296.ed1', '1944.cq1', '1944.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091619, 301891126320, 655477406640, 444, 6227389164], 'label': '46656.ir.648.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '648.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.el1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713309
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dv1', '216.fc1', '324.bm1', '324.da1', '324.db1'], 'contains': ['1296.co1', '1296.cp1', '1296.cx1', '1296.fs1', '1296.gw1', '1296.hl1', '1296.jr1', '1944.cv1', '1944.de1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 1174320, 6227827207], 'label': '46656.ir.648.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.em1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713310
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dv1', '216.fd1', '324.c1', '324.ch1', '324.dc1', '324.dd1', '324.de1', '324.df1', '324.dg1'], 'contains': ['1296.cq1', '1296.cz1', '1296.gy1', '1296.hn1', '1296.kg1', '1944.de1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 6227827207], 'label': '46656.ir.648.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.en1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713311
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dw1', '216.dz1', '324.cu1'], 'contains': ['1296.ct1', '1296.ea1', '1296.ec1', '1944.df1', '1944.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 301891126320, 499, 655477406640, 444], 'label': '46656.ir.648.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '648.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713312
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dx1', '216.ea1', '324.cu1'], 'contains': ['1296.ct1', '1296.eb1', '1296.ed1', '1944.dg1', '1944.dm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 469, 300933848880, 6227827818, 93575951280], 'label': '46656.ir.648.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '648.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ep1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713313
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dy1', '216.eb1', '324.bn1', '324.cs1', '324.cv1'], 'contains': ['1296.cu1', '1296.dg1', '1296.dk1', '1944.dh1', '1944.dl1', '1944.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091120, 499, 269279866800, 37885034880], 'label': '46656.ir.648.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713314
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dz1', '216.ec1', '324.bn1', '324.ct1', '324.cw1'], 'contains': ['1296.cu1', '1296.dh1', '1296.dl1', '1944.dj1', '1944.do1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 301891126320, 1481684400, 39957619, 1481684844], 'label': '46656.ir.648.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.er1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713315
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ea1', '216.ed1', '324.bo1', '324.cs1', '324.cw1'], 'contains': ['1296.cu1', '1296.di1', '1296.dn1', '1944.dk1', '1944.dm1', '1944.dp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 469, 39366316080, 268280812800, 6227827818], 'label': '46656.ir.648.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.es1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713316
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '12.x1', '12.bb1', '12.cb1'], 'contains': ['48.ce1', '72.b1', '72.gi1', '96.i1', '648.is1'], 'core': '72.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 6227827200, 41050800, 1481684400, 39957120, 622713012218, 41051125, 269279866800], 'label': '46656.ir.24.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216713317
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eb1', '216.ed1', '324.bo1', '324.ct1', '324.cv1'], 'contains': ['1296.cu1', '1296.dj1', '1296.dm1', '1944.dk1', '1944.dq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 469, 268280812800, 6227827818, 40323593520], 'label': '46656.ir.648.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.et1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713318
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ec1', '216.eb1', '324.d1', '324.bp1', '324.cx1'], 'contains': ['1296.cv1', '1296.do1', '1296.ds1', '1944.dh1', '1944.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31658054844, 41091120, 268280812800, 499, 37885034880], 'label': '46656.ir.648.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.eu1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713319
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ed1', '216.ec1', '324.d1', '324.bq1', '324.cy1'], 'contains': ['1296.cv1', '1296.dp1', '1296.du1', '1944.di1', '1944.do1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31658054844, 41091120, 268280812800, 39957619, 37885034880], 'label': '46656.ir.648.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ev1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713320
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ee1', '216.ec1', '324.f1', '324.bp1', '324.bq1'], 'contains': ['1296.cv1', '1296.dq1', '1296.dt1', '1944.di1', '1944.dj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 39957619, 1481684844], 'label': '46656.ir.648.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ew1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713321
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ef1', '216.ed1', '324.g1', '324.cx1', '324.cy1'], 'contains': ['1296.cv1', '1296.dr1', '1296.dv1', '1944.dp1', '1944.dq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 469, 39366316080, 1481684400, 6227827818], 'label': '46656.ir.648.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ex1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713322
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eg1', '216.dz1', '216.eb1', '324.cz1'], 'contains': ['1296.cw1', '1296.dw1', '1296.dy1', '1944.dl1', '1944.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 444, 269279866800], 'label': '46656.ir.648.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '648.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ey1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713323
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eh1', '216.ea1', '216.ed1', '324.cz1'], 'contains': ['1296.cw1', '1296.dx1', '1296.dz1', '1944.dm1', '1944.dq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 469, 6227827818, 40323593520, 269279866800], 'label': '46656.ir.648.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '648.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ez1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713324
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ee1', '216.fe1', '324.bm1', '324.dh1', '324.di1'], 'contains': ['1296.cx1', '1296.da1', '1296.dd1', '1296.ji1', '1296.jx1', '1296.ll1', '1296.lt1', '1944.dr1', '1944.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 1174320], 'label': '46656.ir.648.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fa1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713325
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ej1', '216.ef1', '324.bn1', '324.da1', '324.dh1'], 'contains': ['1296.cx1', '1296.dg1', '1296.dl1', '1944.ds1', '1944.eh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 39957120, 499, 1481684400, 1521641964], 'label': '46656.ir.648.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713326
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ek1', '216.eh1', '324.bn1', '324.db1', '324.di1'], 'contains': ['1296.cx1', '1296.dh1', '1296.dk1', '1944.dv1', '1944.ei1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 39957120, 1481684400, 1521641964, 1134499], 'label': '46656.ir.648.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713327
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.h1', '8.i1', '8.j1', '8.k1', '8.l1', '8.m1', '8.n1', '12.bd1', '12.bk1', '36.bw1'], 'core': '24.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 6227827207, 499, 7, 325, 269279866800, 461482882830], 'label': '46656.ir.4.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '4.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216713328
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1'], 'contains': ['48.bq1', '48.cl1', '48.cm1', '72.gj1', '216.jd1', '216.je1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 6267669018, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.24.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '24.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1', 'subgroup_fusion': None, 'weyl_group': '7776.lb'}
  • id: 216713329
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.el1', '216.ek1', '324.bo1', '324.da1', '324.di1'], 'contains': ['1296.cx1', '1296.di1', '1296.dj1', '1944.dx1', '1944.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 268280812800, 1174320, 6227827818], 'label': '46656.ir.648.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713330
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.em1', '216.em1', '324.bo1', '324.db1', '324.dh1'], 'contains': ['1296.cx1', '1296.dm1', '1296.dn1', '1944.dz1', '1944.ek1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 268280812800, 6267744618, 1174320], 'label': '46656.ir.648.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fe1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713331
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.en1', '216.ef1', '324.bp1', '324.cc1', '324.dw1'], 'contains': ['1296.cy1', '1296.do1', '1296.dt1', '1944.ds1', '1944.ed1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 499, 1481684400, 1521641964], 'label': '46656.ir.648.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ff1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713332
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eo1', '216.eh1', '324.bp1', '324.cd1', '324.dx1'], 'contains': ['1296.cy1', '1296.dq1', '1296.ds1', '1944.dv1', '1944.ee1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 1521641964, 1134499], 'label': '46656.ir.648.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713333
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ep1', '216.ei1', '324.bq1', '324.cc1', '324.dx1'], 'contains': ['1296.cy1', '1296.dp1', '1296.dq1', '1944.du1', '1944.ef1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39917299, 39366316080, 39957120, 1481684400, 1521641964], 'label': '46656.ir.648.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713334
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eq1', '216.el1', '324.bq1', '324.cd1', '324.dw1'], 'contains': ['1296.cy1', '1296.dt1', '1296.du1', '1944.dy1', '1944.eg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 41051299, 1481684400, 1521641964], 'label': '46656.ir.648.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '648.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713335
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ee1', '216.ff1', '324.c1', '324.ci1', '324.dj1', '324.dk1', '324.dl1', '324.dm1', '324.dv1'], 'contains': ['1296.cz1', '1296.db1', '1296.kd1', '1296.ki1', '1296.lo1', '1944.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400], 'label': '46656.ir.648.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fj1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713336
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.es1', '216.ef1', '324.d1', '324.cj1', '324.dc1', '324.dj1', '324.dn1', '324.do1', '324.dw1'], 'contains': ['1296.cz1', '1296.do1', '1296.du1', '1944.ed1', '1944.eh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 499, 37885034880], 'label': '46656.ir.648.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fk1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713337
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.eg1', '216.fg1', '324.e1', '324.ch1', '324.dn1', '324.dp1', '324.dq1', '324.dr1', '324.dv1'], 'contains': ['1296.cz1', '1296.kj1', '1296.kl1', '5832.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 6227464327], 'label': '46656.ir.648.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fl1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713338
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eu1', '216.eh1', '324.d1', '324.ck1', '324.dd1', '324.dk1', '324.dp1', '324.ds1', '324.dx1'], 'contains': ['1296.cz1', '1296.dp1', '1296.ds1', '1944.ee1', '1944.ei1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 1134499, 37885034880], 'label': '46656.ir.648.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fm1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713339
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.u1', '12.cc1'], 'contains': ['48.bu1', '48.bv1', '48.bx1', '48.cg1', '48.ch1', '72.gk1', '72.gl1', '72.go1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827207, 1174645], 'label': '46656.ir.24.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713340
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ev1', '216.ei1', '324.f1', '324.cj1', '324.de1', '324.dl1', '324.dq1', '324.dt1', '324.dx1'], 'contains': ['1296.cz1', '1296.dq1', '1944.ef1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 31697931324, 268280812800, 39957120, 37885034880], 'label': '46656.ir.648.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713341
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ej1', '216.fh1', '324.e1', '324.ci1', '324.dg1', '324.do1', '324.ds1', '324.dt1', '324.du1'], 'contains': ['1296.cz1', '1296.kk1', '1296.km1', '5832.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400], 'label': '46656.ir.648.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fo1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713342
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ex1', '216.ek1', '324.g1', '324.cl1', '324.dc1', '324.dk1', '324.dq1', '324.du1', '324.dy1'], 'contains': ['1296.cz1', '1296.dr1', '1944.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 39366316080, 1174320, 1481684400, 6227827818], 'label': '46656.ir.648.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fp1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713343
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ey1', '216.el1', '324.f1', '324.ck1', '324.df1', '324.dm1', '324.dr1', '324.du1', '324.dw1'], 'contains': ['1296.cz1', '1296.dt1', '1944.eg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31697931324, 268280812800, 39957120, 41051299, 37885034880], 'label': '46656.ir.648.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fq1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713344
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ez1', '216.em1', '324.g1', '324.cm1', '324.dd1', '324.dj1', '324.dr1', '324.dt1', '324.dz1'], 'contains': ['1296.cz1', '1296.dv1', '1944.ek1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 6267744618], 'label': '46656.ir.648.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fr1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713345
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fa1', '216.en1', '324.h1', '324.cl1', '324.de1', '324.dm1', '324.dn1', '324.ds1', '324.dz1'], 'contains': ['1296.cz1', '1296.lw1', '5832.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 39366316080, 6227464938, 1174320, 1481684400], 'label': '46656.ir.648.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fs1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713346
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fb1', '216.eo1', '324.h1', '324.cm1', '324.df1', '324.dl1', '324.do1', '324.dp1', '324.dy1'], 'contains': ['1296.cz1', '1296.lx1', '5832.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [469, 39366316080, 1174320, 1481684400, 6267381738], 'label': '46656.ir.648.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ft1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713347
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ep1', '216.fi1', '324.cp1', '324.dg1', '324.dv1', '324.dw1', '324.dx1', '324.dy1', '324.dz1'], 'contains': ['1296.cy1', '1296.cz1', '1296.jv1', '1296.kh1', '1296.kn1', '1944.em1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 7, 37885034880], 'label': '46656.ir.648.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fu1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713348
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fd1', '216.eq1', '324.bi1', '324.cv1', '324.dh1'], 'contains': ['1296.da1', '1296.dg1', '1296.dm1', '1944.en1', '1944.er1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 137, 268280812800, 7], 'label': '46656.ir.648.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713349
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fe1', '216.er1', '324.bi1', '324.cw1', '324.di1'], 'contains': ['1296.da1', '1296.dh1', '1296.di1', '1944.eo1', '1944.es1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 6227827342, 268280812800, 7], 'label': '46656.ir.648.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713350
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.o1', '12.cc1'], 'contains': ['48.bu1', '48.bw1', '48.cd1', '72.gm1', '72.gp1', '216.jf1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40327, 39366316080, 6267381127, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.24.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713351
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ff1', '216.es1', '324.bj1', '324.cv1', '324.di1'], 'contains': ['1296.da1', '1296.dj1', '1296.dk1', '1944.ep1', '1944.et1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6227388862, 6267744007, 39366316080, 268280812800, 7], 'label': '46656.ir.648.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713352
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fg1', '216.et1', '324.bj1', '324.cw1', '324.dh1'], 'contains': ['1296.da1', '1296.dl1', '1296.dn1', '1944.eq1', '1944.eu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174457, 268280812800, 7], 'label': '46656.ir.648.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713353
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fh1', '216.eq1', '324.a1', '324.cx1', '324.dj1'], 'contains': ['1296.db1', '1296.do1', '1296.dv1', '1944.en1', '1944.ex1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684537, 7, 1481684400], 'label': '46656.ir.648.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.fz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713354
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fi1', '216.er1', '324.a1', '324.cy1', '324.dk1'], 'contains': ['1296.db1', '1296.dp1', '1296.dr1', '1944.eo1', '1944.ey1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [43633820302, 6267744007, 39366316080, 7, 1481684400], 'label': '46656.ir.648.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ga1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713355
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fj1', '216.es1', '324.b1', '324.cx1', '324.dk1'], 'contains': ['1296.db1', '1296.dr1', '1296.ds1', '1944.ep1', '1944.ez1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1481684400, 24952072462], 'label': '46656.ir.648.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713356
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fk1', '216.et1', '324.b1', '324.cy1', '324.dj1'], 'contains': ['1296.db1', '1296.du1', '1296.dv1', '1944.eq1', '1944.fa1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 2918003897, 39366316080, 7, 1481684400], 'label': '46656.ir.648.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713357
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fl1', '216.eq1', '216.eu1', '216.ew1', '324.cz1'], 'contains': ['1296.dc1', '1296.dw1', '1296.dz1', '1944.en1', '1944.ev1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 39366316080, 137, 7, 269279866800], 'label': '46656.ir.648.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '648.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713358
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fm1', '216.es1', '216.ev1', '324.cz1'], 'contains': ['1296.dc1', '1296.dx1', '1296.dy1', '1944.ep1', '1944.ew1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6227388862, 6267744007, 39366316080, 7, 269279866800], 'label': '46656.ir.648.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '648.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ge1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713359
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fn1', '216.eq1', '324.bk1', '324.cs1', '324.dh1'], 'contains': ['1296.dd1', '1296.dg1', '1296.dn1', '1944.er1', '1944.ev1', '1944.ex1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 40323593657, 40323593520], 'label': '46656.ir.648.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713360
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fo1', '216.er1', '324.bk1', '324.ct1', '324.di1'], 'contains': ['1296.dd1', '1296.dh1', '1296.dj1', '1944.es1', '1944.ey1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 268280812800, 26911185982, 7, 40323593520], 'label': '46656.ir.648.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '648.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713361
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '12.u1', '12.bx1'], 'contains': ['48.bu1', '48.by1', '48.cc1', '72.gn1', '72.gq1', '216.jh1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39957127, 6227464327, 269279866800], 'label': '46656.ir.24.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713362
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fp1', '216.es1', '324.bl1', '324.cs1', '324.di1'], 'contains': ['1296.dd1', '1296.di1', '1296.dk1', '1944.et1', '1944.ew1', '1944.ez1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 40323593520, 24952072462], 'label': '46656.ir.648.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713363
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fq1', '216.et1', '324.bl1', '324.ct1', '324.dh1'], 'contains': ['1296.dd1', '1296.dl1', '1296.dm1', '1944.eu1', '1944.fa1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 2918003897, 268280812800, 7, 40323593520], 'label': '46656.ir.648.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713364
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fr1', '216.eu1', '324.cu1'], 'contains': ['1296.de1', '1296.ea1', '1296.ed1', '1944.ev1', '1944.fb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 137, 301891126320, 7, 655477406640], 'label': '46656.ir.648.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '648.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gj1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713365
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fs1', '216.ev1', '324.cu1'], 'contains': ['1296.de1', '1296.eb1', '1296.ec1', '1944.ew1', '1944.fc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6227388862, 6267744007, 301891126320, 7, 655477406640], 'label': '46656.ir.648.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '648.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713366
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ft1', '216.ew1'], 'contains': ['1296.df1', '1296.ee1', '1296.ef1', '1944.ev1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 137, 301891126320, 7, 623823424560], 'label': '46656.ir.648.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '648.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gl1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216713367
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ex1', '216.ez1', '216.fj1', '324.br1'], 'contains': ['1296.eg1', '1296.em1', '1296.et1', '1296.fh1', '1296.fx1', '1296.hv1', '1296.la1', '1944.ci1', '1944.fd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 355419187635, 268280812800, 7, 6227827207], 'label': '46656.ir.648.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '648.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713368
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ex1', '216.ey1', '216.fb1', '216.fk1'], 'contains': ['1296.eh1', '1296.en1', '1296.eu1', '1296.fi1', '1296.fy1', '1296.hw1', '1296.lb1', '1944.cj1', '1944.fd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [41091120, 387999647280, 7, 6227827207, 387999647384], 'label': '46656.ir.648.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gn1', 'old_label': '648.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713369
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ex1', '216.fa1', '216.fl1', '324.i1'], 'contains': ['1296.ei1', '1296.eo1', '1296.ev1', '1296.fj1', '1296.fz1', '1296.hx1', '1296.lc1', '1944.ck1', '1944.fd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 6227827207, 435], 'label': '46656.ir.648.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.go1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713370
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fc1', '216.fw1', '324.v1', '324.br1', '324.ea1'], 'contains': ['1296.eg1', '1296.ep1', '1296.fr1', '1296.gj1', '1296.ip1', '1944.cv1', '1944.fe1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 355419187304, 6227827207], 'label': '46656.ir.648.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713371
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.n1', '216.ey1', '216.fx1'], 'contains': ['1296.ek1', '1296.el1', '1296.ew1', '1296.gm1', '1296.ha1', '1296.hp1', '1296.lj1', '1944.cw1', '1944.fd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [41091120, 7, 325, 93536397818, 6227827207], 'label': '46656.ir.648.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '648.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713372
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.t1', '12.cc1'], 'contains': ['48.bv1', '48.ca1', '48.cd1', '72.gr1', '72.gs1', '72.gu1', '216.jk1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.24.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713373
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ez1', '216.fa1', '216.fb1', '216.fy1', '324.i1'], 'contains': ['1296.ej1', '1296.eo1', '1296.es1', '1296.gn1', '1296.hd1', '1296.ia1', '1296.kq1', '1944.cx1', '1944.fd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 7, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.648.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713374
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fc1', '216.fd1', '216.gf1', '324.i1'], 'contains': ['1296.ei1', '1296.ej1', '1296.er1', '1296.fu1', '1296.gx1', '1296.hk1', '1296.js1', '1944.de1', '1944.fe1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 6227827207, 435], 'label': '46656.ir.648.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '648.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713375
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fe1', '216.gs1', '324.w1', '324.br1', '324.ed1'], 'contains': ['1296.ep1', '1296.et1', '1296.ij1', '1296.iu1', '1296.lk1', '1944.dr1', '1944.ff1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 355419187635, 268280812800, 7, 1174320], 'label': '46656.ir.648.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gt1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713376
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.fh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cw1', '216.gu1', '324.v1', '324.bt1', '324.ed1'], 'contains': ['1296.ep1', '1296.ix1', '1296.iz1', '1944.dt1', '1944.fg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 355419187304], 'label': '46656.ir.648.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713377
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cx1', '216.gx1', '324.w1', '324.bt1', '324.ea1'], 'contains': ['1296.ep1', '1296.iy1', '1296.ja1', '1944.dw1', '1944.fh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381127, 268280812800, 7, 1174320, 355419187304], 'label': '46656.ir.648.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gv1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713378
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fe1', '216.ff1', '216.hd1', '324.i1'], 'contains': ['1296.er1', '1296.es1', '1296.ev1', '1296.jh1', '1296.jw1', '1296.kt1', '1296.ln1', '1944.ec1', '1944.ff1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 104], 'label': '46656.ir.648.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713379
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ba1', '216.hm1', '324.bs1', '324.eb1', '324.ec1'], 'contains': ['1296.jz1', '1944.el1', '1944.fi1', '2592.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41050800, 7, 41051125, 641394472778, 31697930880], 'label': '46656.ir.648.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '648.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216713380
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fi1', '216.hn1', '324.ce1', '324.ea1', '324.ed1'], 'contains': ['1296.ep1', '1296.eq1', '1296.ir1', '1296.jt1', '1296.kc1', '1944.em1', '1944.fi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 41050800, 7, 31697930984, 37885034880], 'label': '46656.ir.648.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713400
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ha1', '216.hl1', '324.p1', '324.bc1', '324.eh1', '324.el1', '324.et1', '324.ev1', '324.fb1'], 'contains': ['1296.ez1', '1296.ff1', '5832.bl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6267744618, 7, 104], 'label': '46656.ir.648.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.hq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hq1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713381
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fj1', '216.fk1', '216.fl1', '216.fx1', '216.fy1', '324.l1', '324.ee1', '324.ef1'], 'contains': ['1296.ex1', '1296.ey1', '1296.fa1', '1296.fg1', '1296.gd1', '1296.hr1', '1296.ks1', '1944.fd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 7, 325, 6227827207, 104], 'label': '46656.ir.648.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.gz1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713382
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fm1', '216.fq1', '216.fs1', '216.fz1', '216.gd1', '324.j1', '324.ee1', '324.eg1'], 'contains': ['1296.a1', '1296.ex1', '1296.fc1', '5832.v1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6227827207, 499, 7, 104, 325], 'label': '46656.ir.648.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '648.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ha1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713383
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '12.u1', '12.ca1'], 'contains': ['48.bv1', '48.cb1', '48.cc1', '72.gt1', '72.gv1', '216.jl1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 6267381120, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.24.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713384
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fn1', '216.ft1', '216.ga1', '324.j1', '324.ef1', '324.eh1'], 'contains': ['1296.ex1', '1296.fb1', '1296.ff1', '5832.w1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39917299, 7, 325, 6227827207, 104], 'label': '46656.ir.648.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '648.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hb1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713385
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fo1', '216.fu1', '216.gb1', '324.k1', '324.ef1', '324.eg1'], 'contains': ['1296.ex1', '1296.fc1', '1296.fe1', '5832.x1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174819, 6227827207, 7, 104, 325], 'label': '46656.ir.648.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '648.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hc1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713386
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fp1', '216.fr1', '216.fv1', '216.gc1', '216.ge1', '324.k1', '324.ee1', '324.eh1'], 'contains': ['1296.ex1', '1296.fd1', '1296.ff1', '5832.y1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091619, 7, 325, 6227827207, 104], 'label': '46656.ir.648.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hd1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713387
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fw1', '216.gf1', '324.l1', '324.x1', '324.eg1', '324.eh1', '324.ei1', '324.ej1', '324.ek1'], 'contains': ['1296.ex1', '1296.ez1', '1296.fw1', '1296.gl1', '1296.iq1', '1944.fe1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 7, 104], 'label': '46656.ir.648.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.he1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713388
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gg1', '216.gi1', '216.gm1', '216.go1', '324.m1', '324.ee1'], 'contains': ['1296.a1', '1296.ey1', '1296.fd1', '5832.ba1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 499, 7, 325, 104], 'label': '46656.ir.648.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '648.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hf1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713389
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gj1', '216.gk1', '216.gp1', '324.m1', '324.o1', '324.ef1'], 'contains': ['1296.ey1', '1296.fb1', '1296.fe1', '5832.bb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41091120, 7, 325, 39957619, 104], 'label': '46656.ir.648.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hg1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713390
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gh1', '216.gl1', '216.gn1', '216.gq1', '216.gr1', '324.p1', '324.ee1', '324.ef1'], 'contains': ['1296.ey1', '1296.fc1', '1296.ff1', '5832.bc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 7, 325, 6227827818, 104], 'label': '46656.ir.648.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hh1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713391
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gs1', '216.hd1', '324.l1', '324.y1', '324.el1', '324.em1', '324.en1', '324.eo1', '324.ex1'], 'contains': ['1296.ez1', '1296.fa1', '1296.ii1', '1296.iw1', '1296.kv1', '1944.ff1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 7, 1174320, 104, 1174645], 'label': '46656.ir.648.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.hi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hi1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713392
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gt1', '216.he1', '216.hi1', '324.m1', '324.z1', '324.eg1', '324.el1', '324.ep1', '324.eq1', '324.ey1'], 'contains': ['1296.a1', '1296.ez1', '1296.fe1', '5832.be1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 499, 7, 325, 39957224], 'label': '46656.ir.648.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.hj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hj1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713393
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.et1', '216.gu1', '324.n1', '324.x1', '324.ep1', '324.er1', '324.es1', '324.et1', '324.ex1'], 'contains': ['1296.ez1', '1296.jd1', '1296.jf1', '1944.fg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 1174320, 6227464327, 104, 1174645], 'label': '46656.ir.648.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.hk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hk1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713394
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.n1', '12.cc1'], 'contains': ['48.bw1', '48.bx1', '48.ca1', '72.gw1', '72.gy1', '216.ji1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 40327, 269279866800], 'label': '46656.ir.24.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713395
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gw1', '216.hf1', '216.hj1', '324.m1', '324.ba1', '324.eh1', '324.em1', '324.er1', '324.eu1', '324.ez1'], 'contains': ['1296.ez1', '1296.fb1', '1296.fd1', '5832.bg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 7, 325, 39957224, 1134499], 'label': '46656.ir.648.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.hl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hl1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713396
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gv1', '216.hg1', '324.o1', '324.z1', '324.ei1', '324.en1', '324.es1', '324.ev1', '324.ez1'], 'contains': ['1296.ez1', '1296.fb1', '5832.bh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39957120, 7, 325, 39957224], 'label': '46656.ir.648.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.hm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hm1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713397
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ew1', '216.gx1', '324.n1', '324.y1', '324.ek1', '324.eq1', '324.eu1', '324.ev1', '324.ew1'], 'contains': ['1296.ez1', '1296.je1', '1296.jg1', '1944.fh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381127, 7, 1174320, 104, 1174645], 'label': '46656.ir.648.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.hn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hn1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713398
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gy1', '216.hk1', '324.p1', '324.bb1', '324.eg1', '324.em1', '324.es1', '324.ew1', '324.fa1'], 'contains': ['1296.ez1', '1296.fc1', '5832.bj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 1174320, 6227827818, 104, 1174645], 'label': '46656.ir.648.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.ho1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ho1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713399
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gz1', '216.hh1', '324.o1', '324.ba1', '324.ej1', '324.eo1', '324.et1', '324.ew1', '324.ey1'], 'contains': ['1296.ez1', '1296.fe1', '5832.bk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41051299, 7, 325, 39957224], 'label': '46656.ir.648.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.hp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hp1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713401
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fa1', '216.hb1', '324.q1', '324.bb1', '324.ei1', '324.eo1', '324.ep1', '324.eu1', '324.fb1'], 'contains': ['1296.ez1', '1296.lu1', '5832.bm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6227464938, 7, 1174320, 104, 1174645], 'label': '46656.ir.648.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.hr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hr1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713402
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.fb1', '216.hc1', '324.q1', '324.bc1', '324.ej1', '324.en1', '324.eq1', '324.er1', '324.fa1'], 'contains': ['1296.ez1', '1296.lv1', '5832.bn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [7, 1174320, 6267381738, 104, 1174645], 'label': '46656.ir.648.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.hs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hs1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713403
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hm1', '216.hn1', '324.bu1', '324.ek1', '324.ex1', '324.ey1', '324.ez1', '324.fa1', '324.fb1'], 'contains': ['1296.ez1', '1296.it1', '1296.kb1', '1944.fi1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 7, 41051125, 39957224], 'label': '46656.ir.648.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '648.ht1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ht1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713404
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ho1', '216.hs1', '216.hw1', '216.hy1', '216.ic1', '324.j1', '324.ee1', '324.el1'], 'contains': ['1296.a1', '1296.fa1', '1296.ff1', '5832.bp1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 499, 7, 325, 104], 'label': '46656.ir.648.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '648.hu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hu1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713405
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.o1', '12.ca1'], 'contains': ['48.bw1', '48.bz1', '48.cb1', '72.gx1', '72.gz1', '216.jj1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267381120, 40327, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.24.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713406
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hp1', '216.ht1', '216.hz1', '324.j1', '324.ef1', '324.em1'], 'contains': ['1296.fa1', '1296.fb1', '1296.fc1', '5832.bq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 7, 325, 6227827818, 104], 'label': '46656.ir.648.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '648.hv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hv1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713407
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hq1', '216.hu1', '216.hx1', '216.ia1', '216.id1', '324.k1', '324.ee1', '324.em1'], 'contains': ['1296.fa1', '1296.fc1', '1296.fd1', '5832.br1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 7, 325, 6227389338, 104], 'label': '46656.ir.648.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hw1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713408
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hr1', '216.hv1', '216.ib1', '324.k1', '324.ef1', '324.el1'], 'contains': ['1296.fa1', '1296.fe1', '1296.ff1', '5832.bs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 1174819, 7, 325, 104], 'label': '46656.ir.648.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hx1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713409
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ie1', '216.if1', '216.il1', '324.l1'], 'contains': ['1296.fg1', '1296.fq1', '1296.fw1', '1296.ho1', '1296.hr1', '1296.kp1', '1296.kv1', '1944.fj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 1174327, 325, 6227827207, 104], 'label': '46656.ir.648.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '648.hy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hy1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713410
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ie1', '216.ig1', '216.im1', '324.i1'], 'contains': ['1296.fj1', '1296.fl1', '1296.fu1', '1296.ht1', '1296.ia1', '1296.ky1', '1296.ln1', '1944.fj1', '1944.fk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 1174327, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.648.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.hz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.hz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713411
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.if1', '216.ig1', '216.in1', '324.br1'], 'contains': ['1296.fh1', '1296.fo1', '1296.fr1', '1296.hu1', '1296.hv1', '1296.kz1', '1296.lk1', '1944.fj1', '1944.fl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 355419187635, 1174327, 268280812800, 6227827207], 'label': '46656.ir.648.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '648.ia1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ia1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713412
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ig1', '216.io1', '324.bm1'], 'contains': ['1296.fk1', '1296.fm1', '1296.fs1', '1296.ic1', '1296.if1', '1296.lq1', '1296.lt1', '1944.fk1', '1944.fl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 1174327, 268280812800, 40323593520, 6227827207], 'label': '46656.ir.648.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.ib1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ib1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713413
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gc1', '216.ih1', '324.v1', '324.bw1', '324.fd1'], 'contains': ['1296.gj1', '1296.ik1', '1296.iz1', '1944.fm1', '1944.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 40327, 268280812800, 1174320, 6227827200], 'label': '46656.ir.648.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.ic1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ic1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216713414
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ii1', '216.ip1', '324.bd1', '324.br1', '324.fd1'], 'contains': ['1296.fo1', '1296.fx1', '1296.gj1', '1296.il1', '1296.iu1', '1944.fn1', '1944.fo1', '1944.fp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 355419187635, 268280812800, 1174320, 6227827200], 'label': '46656.ir.648.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.id1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.id1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713415
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ii1', '216.iq1', '324.be1'], 'contains': ['1296.fp1', '1296.ga1', '1296.gk1', '1296.im1', '1296.iv1', '1944.fn1', '1944.fp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 268281987445, 1174320, 6227827200, 355419187304], 'label': '46656.ir.648.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '648.ie1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ie1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713416
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.u1', '12.bj1'], 'contains': ['48.bx1', '48.by1', '48.cb1', '72.ha1', '72.hb1', '216.jm1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 39957127, 269279866800], 'label': '46656.ir.24.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713417
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ii1', '216.ir1', '324.l1', '324.bf1', '324.fc1'], 'contains': ['1296.fq1', '1296.gd1', '1296.gl1', '1296.in1', '1296.iw1', '1944.fn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 1174320, 6227827200, 104, 1174645], 'label': '46656.ir.648.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.if1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.if1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713418
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gd1', '216.ih1', '324.r1', '324.x1', '324.fc1'], 'contains': ['1296.gl1', '1296.io1', '1296.jf1', '1944.fq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 1174320, 6227827200, 104, 1174645], 'label': '46656.ir.648.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.ig1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ig1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713419
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gf1', '216.ij1', '324.bd1', '324.bw1', '324.ea1'], 'contains': ['1296.gj1', '1296.ir1', '1296.ja1', '1944.fr1', '1944.fs1', '1944.ft1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 6267381127, 268280812800, 1174320, 39957127], 'label': '46656.ir.648.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.ih1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ih1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713420
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ge1', '216.ij1', '324.be1'], 'contains': ['1296.gk1', '1296.is1', '1296.jc1', '1944.fr1', '1944.ft1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267381127, 1174320, 268280812904, 39957127, 1174645], 'label': '46656.ir.648.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '648.ii1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ii1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 216713421
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gg1', '216.ij1', '324.r1', '324.bf1', '324.ek1'], 'contains': ['1296.gl1', '1296.it1', '1296.jg1', '1944.fr1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381127, 1174320, 39957127, 104, 1174645], 'label': '46656.ir.648.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.ij1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ij1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713422
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gh1', '216.ik1', '216.is1', '324.bv1', '324.ek1', '324.fc1'], 'contains': ['1296.gl1', '1296.je1', '1296.kb1', '1944.fu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 6227827200], 'label': '46656.ir.648.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.ik1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ik1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216713423
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gi1', '216.ik1', '324.cf1', '324.ea1', '324.fd1'], 'contains': ['1296.gj1', '1296.iy1', '1296.kc1', '1944.fu1', '1944.fv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 6227827200], 'label': '46656.ir.648.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '648.il1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.il1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216713424
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.il1', '216.im1', '216.in1', '324.i1'], 'contains': ['1296.gn1', '1296.gt1', '1296.gx1', '1296.ht1', '1296.hx1', '1296.ko1', '1296.kt1', '1944.fj1', '1944.fw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 6227827207, 435], 'label': '46656.ir.648.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.im1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.im1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713425
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.im1', '216.io1', '324.c1'], 'contains': ['1296.gq1', '1296.gs1', '1296.gy1', '1296.ib1', '1296.ig1', '1296.kw1', '1296.lo1', '1944.fk1', '1944.fw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 1481684400, 6227827207], 'label': '46656.ir.648.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '648.in1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.in1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713426
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.in1', '216.io1', '324.bm1'], 'contains': ['1296.gp1', '1296.gu1', '1296.gw1', '1296.ic1', '1296.ie1', '1296.kx1', '1296.ll1', '1944.fl1', '1944.fw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 268280812800, 6227827207], 'label': '46656.ir.648.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.io1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.io1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713427
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '12.t1', '12.bx1'], 'contains': ['48.by1', '48.bz1', '48.ca1', '72.hc1', '72.hd1', '72.he1', '216.jn1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 39957127, 1174645], 'label': '46656.ir.24.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713428
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ip1', '216.iq1', '216.ir1', '216.it1', '324.i1'], 'contains': ['1296.fl1', '1296.fz1', '1296.gt1', '1296.hd1', '1296.hk1', '1296.jk1', '1296.jw1', '1944.fn1', '1944.fx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 6227827200, 104], 'label': '46656.ir.648.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.ip1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ip1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713429
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ip1', '216.iv1', '324.bm1'], 'contains': ['1296.fm1', '1296.ge1', '1296.gu1', '1296.he1', '1296.hl1', '1296.jl1', '1296.jx1', '1944.fo1', '1944.fx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 1174320, 6227827200], 'label': '46656.ir.648.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.iq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713430
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ip1', '216.iq1', '216.iu1'], 'contains': ['1296.fn1', '1296.gh1', '1296.gv1', '1296.hh1', '1296.hm1', '1296.jo1', '1296.jy1', '1944.fp1', '1944.fx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [39916807, 355419187635, 39366316080, 1174320, 6227827200], 'label': '46656.ir.648.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '648.ir1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ir1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713431
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cl1', '216.is1', '324.bx1', '324.eb1', '324.fe1'], 'contains': ['1296.jz1', '1944.fu1', '1944.fy1', '2592.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [641394472778, 269202528325, 299859033600, 6227827200, 269202528000], 'label': '46656.ir.648.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '648.is1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.is1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216713432
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.it1', '216.iu1', '216.iv1', '324.c1', '324.cn1', '324.ff1'], 'contains': ['1296.gs1', '1296.hf1', '1296.hn1', '1296.ke1', '1296.ki1', '1944.fx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 6227827200], 'label': '46656.ir.648.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.it1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.it1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713433
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.iw1', '216.ix1', '324.s1', '324.ch1', '324.ff1'], 'contains': ['1296.hn1', '1296.kf1', '1296.kl1', '5832.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 39366316080, 1174320, 1481684400, 6227827200], 'label': '46656.ir.648.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.iu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iu1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713434
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.iy1', '216.iz1', '216.ja1', '324.s1', '324.cn1', '324.dg1'], 'contains': ['1296.hn1', '1296.kh1', '1296.km1', '5832.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 39957127], 'label': '46656.ir.648.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.iv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iv1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713435
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jb1', '216.jc1', '324.cq1', '324.dg1', '324.ff1'], 'contains': ['1296.hn1', '1296.kk1', '1296.kn1', '5832.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 6227827200], 'label': '46656.ir.648.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.iw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iw1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713436
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gj1', '216.jd1', '324.q1'], 'contains': ['1296.ho1', '1296.lu1', '1296.lv1', '5832.by1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 1174327, 6267669018, 325, 104], 'label': '46656.ir.648.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.g1', 'old_label': '648.ix1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ix1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713437
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gj1', '216.je1', '324.h1'], 'contains': ['1296.ib1', '1296.lw1', '1296.lx1', '5832.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 39366316080, 6267669018, 1481684400, 1174789], 'label': '46656.ir.648.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '648.iy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iy1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713438
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['7776.t1', '7776.bx1', '7776.by1', '7776.bl1', '7776.cv1', '7776.cw1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.c1', '12.g1', '12.i1', '12.p1', '12.q1', '18.k1', '54.z1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 499, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.6.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1', '12.b1', '12.c1', '24.b1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '46656.ir', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216713439
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '12.w1', '12.bx1', '12.cc1'], 'contains': ['48.d1', '48.bu1', '48.ca1', '72.hf1', '72.hj1', '216.ju1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267744000, 41050800, 1481684400, 39957120, 41051125, 269279866800, 1521641624], 'label': '46656.ir.24.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216713440
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jg1', '216.jo1', '324.l1', '324.bg1', '324.fg1'], 'contains': ['1296.ii1', '1296.in1', '1296.iq1', '1296.kp1', '1296.ks1', '1944.ga1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 1174320, 6227827207, 104, 1174645], 'label': '46656.ir.648.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.iz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.iz1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713441
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gm1', '216.jf1', '324.r1', '324.y1', '324.fg1'], 'contains': ['1296.ii1', '1296.io1', '1296.jg1', '1944.gb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [40327, 6267381127, 1174320, 104, 1174645], 'label': '46656.ir.648.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.ja1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ja1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713442
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gn1', '216.jh1', '324.r1', '324.bg1', '324.ex1'], 'contains': ['1296.ii1', '1296.it1', '1296.jf1', '1944.gc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174320, 6227464327, 39957127, 104, 1174645], 'label': '46656.ir.648.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.jb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jb1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713443
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gp1', '216.jf1', '324.w1', '324.bw1', '324.fi1'], 'contains': ['1296.ij1', '1296.ik1', '1296.ja1', '1944.gb1', '1944.gd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 40327, 6267381127, 268280812800, 1174320], 'label': '46656.ir.648.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.jc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713444
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jg1', '216.jq1', '324.bh1', '324.br1', '324.fi1'], 'contains': ['1296.ij1', '1296.il1', '1296.ip1', '1296.kz1', '1296.la1', '1944.ga1', '1944.ge1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 355419187635, 268280812800, 1174320, 6227827207], 'label': '46656.ir.648.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.jd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713445
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gq1', '216.jh1', '324.bh1', '324.bw1', '324.ed1'], 'contains': ['1296.ij1', '1296.ir1', '1296.iz1', '1944.gc1', '1944.gf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 1174320, 6227464327, 355419187304, 39957127], 'label': '46656.ir.648.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.je1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.je1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713446
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gw1', '216.ji1', '324.v1', '324.cb1', '324.fi1'], 'contains': ['1296.ik1', '1296.ip1', '1296.ix1', '1944.gg1', '1944.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 40327, 268280812800, 1174320, 6227827207], 'label': '46656.ir.648.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.jf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216713447
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gx1', '216.jj1', '324.w1', '324.cb1', '324.fd1'], 'contains': ['1296.ik1', '1296.iu1', '1296.iy1', '1944.gh1', '1944.go1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381120, 355419187635, 40327, 268280812800, 1174320], 'label': '46656.ir.648.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.jg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713448
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gs1', '216.jk1', '324.bd1', '324.bt1', '324.fi1'], 'contains': ['1296.il1', '1296.ix1', '1296.ja1', '1944.gi1', '1944.gk1', '1944.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 355419187635, 6267381127, 268280812800, 1174320], 'label': '46656.ir.648.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.jh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713449
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gt1', '216.jl1', '324.bh1', '324.bt1', '324.fd1'], 'contains': ['1296.il1', '1296.iy1', '1296.iz1', '1944.gj1', '1944.gl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 6267381120, 355419187635, 268280812800, 1174320], 'label': '46656.ir.648.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.ji1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ji1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713450
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '12.x1', '12.bc1', '12.cd1'], 'contains': ['48.ce1', '72.c1', '72.hj1', '96.s1', '648.jv1'], 'core': '72.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [624190336641, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6267744000, 1521641624], 'label': '46656.ir.24.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216713451
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gr1', '216.jk1', '324.be1'], 'contains': ['1296.im1', '1296.jb1', '1296.jc1', '1944.gi1', '1944.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 6267381127, 1174320, 355419187304, 1174645], 'label': '46656.ir.648.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '648.jj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jj1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713452
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gu1', '216.jk1', '324.n1', '324.bf1', '324.fg1'], 'contains': ['1296.in1', '1296.jd1', '1296.jg1', '1944.gi1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 6267381127, 1174320, 104, 1174645], 'label': '46656.ir.648.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.jk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jk1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713453
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gv1', '216.jl1', '324.n1', '324.bg1', '324.fc1'], 'contains': ['1296.in1', '1296.je1', '1296.jf1', '1944.gj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 6267381120, 1174320, 104, 1174645], 'label': '46656.ir.648.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.jl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jl1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713454
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gy1', '216.ji1', '324.t1', '324.x1', '324.fg1'], 'contains': ['1296.io1', '1296.iq1', '1296.jd1', '1944.gn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 1174320, 6227827207, 104, 1174645], 'label': '46656.ir.648.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '648.jm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jm1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713455
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gz1', '216.jj1', '324.t1', '324.y1', '324.fc1'], 'contains': ['1296.io1', '1296.iw1', '1296.je1', '1944.go1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 40327, 1174320, 104, 1174645], 'label': '46656.ir.648.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.jn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jn1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713456
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ha1', '216.jm1', '324.bh1', '324.cb1', '324.ea1'], 'contains': ['1296.ip1', '1296.ir1', '1296.iy1', '1944.gp1', '1944.gq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 1174320, 355419187304, 6227827207, 39957127], 'label': '46656.ir.648.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.jo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jo1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713457
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hb1', '216.jm1', '324.t1', '324.bg1', '324.ek1'], 'contains': ['1296.iq1', '1296.it1', '1296.je1', '1944.gq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174645, 1174320, 6227827207, 39957127, 104], 'label': '46656.ir.648.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.jp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jp1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713458
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hd1', '216.jn1', '324.bd1', '324.cb1', '324.ed1'], 'contains': ['1296.ir1', '1296.iu1', '1296.ix1', '1944.gr1', '1944.gs1', '1944.gt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 268280812800, 1174320, 355419187304, 39957127], 'label': '46656.ir.648.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.jq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713459
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hc1', '216.jn1', '324.be1'], 'contains': ['1296.is1', '1296.iv1', '1296.jb1', '1944.gr1', '1944.gt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 268281987445, 1174320, 355419187304, 39957127], 'label': '46656.ir.648.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '648.jr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jr1', 'subgroup_fusion': None, 'weyl_group': '72.49'}
  • id: 216713520
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.j1', '288.o1', '432.dz1'], 'contains': ['1728.k1', '2592.t1', '2592.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [622713012218, 7, 325, 388956924720], 'label': '46656.ir.864.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bw1', 'old_label': '864.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.w1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 216713460
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.he1', '216.jn1', '324.t1', '324.bf1', '324.ex1'], 'contains': ['1296.it1', '1296.iw1', '1296.jd1', '1944.gr1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 1174320, 39957127, 104, 1174645], 'label': '46656.ir.648.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.js1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.js1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713461
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '12.v1', '12.cb1', '12.cd1'], 'contains': ['48.ce1', '72.hk1', '72.hl1', '96.z1', '648.jx1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 622713012218, 41051125, 39916807, 269279866800], 'label': '46656.ir.24.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216713462
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hf1', '216.jp1', '216.ju1', '324.bv1', '324.ex1', '324.fg1'], 'contains': ['1296.ii1', '1296.jd1', '1296.kb1', '1944.gu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 6267744000], 'label': '46656.ir.648.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.jt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jt1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 216713463
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jo1', '216.jq1', '216.jy1', '324.i1'], 'contains': ['1296.jh1', '1296.jk1', '1296.js1', '1296.ko1', '1296.kq1', '1296.ky1', '1296.lc1', '1944.ga1', '1944.gv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 6227827207, 104], 'label': '46656.ir.648.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '648.ju1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ju1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713464
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cx1', '216.jp1', '324.bx1', '324.ec1', '324.fh1'], 'contains': ['1296.jz1', '1944.gu1', '1944.gw1', '2592.cv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 41050800, 39957224, 93536397441, 6267744000], 'label': '46656.ir.648.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '648.jv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jv1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216713465
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jq1', '216.kb1', '324.bm1'], 'contains': ['1296.ji1', '1296.jl1', '1296.jr1', '1296.kx1', '1296.ld1', '1296.lq1', '1296.lr1', '1944.ge1', '1944.gv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 1174320, 6227827207], 'label': '46656.ir.648.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '648.jw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713466
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cy1', '216.jr1', '324.bs1', '324.fe1', '324.fh1'], 'contains': ['1296.jz1', '1944.gx1', '1944.gy1', '2592.eu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 39957120, 39957224, 132379435521, 1520467200], 'label': '46656.ir.648.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '648.jx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jx1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216713467
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jr1', '216.jv1', '324.bu1', '324.fc1', '324.fg1'], 'contains': ['1296.in1', '1296.io1', '1296.kb1', '1944.gy1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 41051125, 39957224], 'label': '46656.ir.648.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '648.jy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jy1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713468
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cz1', '216.js1', '324.by1', '324.eb1', '324.fh1'], 'contains': ['1296.jz1', '1944.gz1', '1944.ha1', '1944.hb1', '2592.ed1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [641394472778, 269202528325, 299859033600, 269202528000, 6227827207], 'label': '46656.ir.648.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '648.jz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.jz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216713469
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.da1', '216.js1', '324.bz1'], 'contains': ['1296.ka1', '1944.gz1', '1944.hb1', '2592.ee1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1520467525, 722937882588, 37924992000, 1520467200, 6227827207], 'label': '46656.ir.648.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.bz1', 'old_label': '648.ka1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ka1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 216713470
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hh1', '216.js1', '216.jw1', '324.ca1', '324.ek1', '324.fg1'], 'contains': ['1296.iq1', '1296.jg1', '1296.kb1', '1944.gz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 6227827207], 'label': '46656.ir.648.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.kb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kb1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713471
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dc1', '216.jt1', '324.by1', '324.ec1', '324.fe1'], 'contains': ['1296.jz1', '1944.hc1', '1944.hd1', '1944.he1', '2592.ge1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 39957224, 93536397441], 'label': '46656.ir.648.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '648.kc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kc1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 216713472
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '12.y1', '12.bb1', '12.cd1'], 'contains': ['48.ce1', '72.hm1', '72.hn1', '72.ho1', '96.u1', '648.jz1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [624190336641, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207, 1521641624], 'label': '46656.ir.24.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216713473
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dd1', '216.jt1', '324.bz1'], 'contains': ['1296.ka1', '1944.hc1', '1944.he1', '2592.gf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1520467525, 6267744007, 722937882588, 37924992000, 1520467200], 'label': '46656.ir.648.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.bz1', 'old_label': '648.kd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kd1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 216713474
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hi1', '216.jt1', '216.jx1', '324.ca1', '324.ex1', '324.fc1'], 'contains': ['1296.iw1', '1296.jf1', '1296.kb1', '1944.hc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 41051125, 39957224], 'label': '46656.ir.648.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.ke1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ke1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216713475
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hj1', '216.ju1', '324.cf1', '324.ed1', '324.fi1'], 'contains': ['1296.ij1', '1296.ix1', '1296.kc1', '1944.gu1', '1944.hf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 6267744000], 'label': '46656.ir.648.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '648.kf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 216713476
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jv1', '216.kt1', '324.ce1', '324.fd1', '324.fi1'], 'contains': ['1296.ik1', '1296.il1', '1296.jj1', '1296.jq1', '1296.kc1', '1944.gy1', '1944.hg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 31697931315, 37885034880], 'label': '46656.ir.648.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.kg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713477
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hm1', '216.jw1', '324.cg1', '324.ea1', '324.fi1'], 'contains': ['1296.ip1', '1296.ja1', '1296.kc1', '1944.gz1', '1944.hh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355459144755, 268280812800, 39957120, 41050800, 6227827207], 'label': '46656.ir.648.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.kh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713478
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hp1', '216.jx1', '324.cg1', '324.ed1', '324.fd1'], 'contains': ['1296.iu1', '1296.iz1', '1296.kc1', '1944.hc1', '1944.hi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 268280812800, 39957120, 41050800, 355459144424], 'label': '46656.ir.648.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '648.ki1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ki1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216713479
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jy1', '216.kb1', '324.c1', '324.co1', '324.fj1'], 'contains': ['1296.kd1', '1296.ke1', '1296.kg1', '1296.kw1', '1296.lf1', '1944.gv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 6227827207], 'label': '46656.ir.648.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kj1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713480
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jz1', '216.kc1', '324.s1', '324.ci1', '324.fj1'], 'contains': ['1296.kd1', '1296.kf1', '1296.km1', '5832.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [40327, 39366316080, 6267381127, 1174320, 1481684400], 'label': '46656.ir.648.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kk1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713481
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ka1', '216.kd1', '324.s1', '324.co1', '324.dv1'], 'contains': ['1296.kd1', '1296.kh1', '1296.kl1', '5832.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227464327, 39957127], 'label': '46656.ir.648.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kl1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713482
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ke1', '216.kg1', '216.kh1', '324.e1', '324.cn1', '324.fj1'], 'contains': ['1296.ke1', '1296.kj1', '1296.km1', '5832.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 1174320, 1481684400], 'label': '46656.ir.648.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.km1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.km1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713483
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '12.z1'], 'contains': ['48.cf1', '72.hm1', '72.ho1', '96.v1', '648.ka1'], 'core': '432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 461333739315, 39957120, 41050800, 1481684400, 269279866800, 6227827207, 1521641624], 'label': '46656.ir.24.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.z1', 'old_label': '24.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1', 'subgroup_fusion': None, 'weyl_group': '3888.bx'}
  • id: 216713484
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kf1', '216.ki1', '324.e1', '324.co1', '324.ff1'], 'contains': ['1296.ke1', '1296.kk1', '1296.kl1', '5832.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 6267381120, 39366316080, 1174320, 1481684400], 'label': '46656.ir.648.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713485
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kj1', '216.kl1', '324.u1', '324.ch1', '324.fj1'], 'contains': ['1296.kf1', '1296.kg1', '1296.kj1', '5832.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40327, 39366316080, 1174320, 1481684400, 6227827207], 'label': '46656.ir.648.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '648.ko1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ko1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713486
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kk1', '216.km1', '324.u1', '324.ci1', '324.ff1'], 'contains': ['1296.kf1', '1296.ki1', '1296.kk1', '5832.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 40327, 39366316080, 1174320, 1481684400], 'label': '46656.ir.648.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kp1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713487
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kn1', '216.ko1', '324.u1', '324.co1', '324.dg1'], 'contains': ['1296.kg1', '1296.kh1', '1296.kk1', '5832.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227827207, 39957127], 'label': '46656.ir.648.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kq1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713488
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kp1', '216.kq1', '216.kr1', '324.u1', '324.cn1', '324.dv1'], 'contains': ['1296.kh1', '1296.ki1', '1296.kj1', '5832.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 39957127], 'label': '46656.ir.648.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kr1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713489
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ks1', '216.kw1', '324.cq1', '324.dv1', '324.fj1'], 'contains': ['1296.kd1', '1296.kj1', '1296.kn1', '5832.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 6267744000], 'label': '46656.ir.648.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.ks1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ks1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713490
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kt1', '216.kx1', '324.cp1', '324.ff1', '324.fj1'], 'contains': ['1296.jn1', '1296.jp1', '1296.ke1', '1296.kf1', '1296.kn1', '1944.hg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 37885034880], 'label': '46656.ir.648.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kt1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713491
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ku1', '216.ky1', '324.cr1', '324.dg1', '324.fj1'], 'contains': ['1296.kg1', '1296.km1', '1296.kn1', '5832.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 6227827207], 'label': '46656.ir.648.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.ku1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.ku1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713492
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '648.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kv1', '216.kz1', '324.cr1', '324.dv1', '324.ff1'], 'contains': ['1296.ki1', '1296.kl1', '1296.kn1', '5832.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 1481684400], 'label': '46656.ir.648.kv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '648.kv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.kv1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713493
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '729.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1', '243.a1', '243.b1'], 'contains': ['1458.a1', '1458.b1', '1458.c1', '1458.d1', '1458.e1', '1458.f1', '1458.g1', '1458.h1', '1458.i1', '1458.j1', '1458.k1', '1458.l1', '1458.m1', '1458.n1', '1458.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 499, 39957564, 39916800, 443609999724, 2957880240], 'label': '46656.ir.729.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '729.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713494
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '12.ba1', '12.bj1', '12.cc1'], 'contains': ['48.d1', '48.bx1', '48.cd1', '72.hh1', '72.hm1', '216.jw1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 6227827207, 1521641624], 'label': '46656.ir.24.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713495
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['54.bh1', '54.bj1', '54.bk1', '54.bi1'], 'conjugacy_class_count': 1, 'contained_in': ['288.bh1', '288.bi1', '288.bj1', '432.bm1', '432.cr1', '432.gp1', '432.is1', '432.it1'], 'contains': ['1728.a1', '2592.cc1', '2592.cd1', '2592.ce1'], 'core': '864.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 269279866800], 'label': '46656.ir.864.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': ['96.b1', '216.a1'], 'normal_contains': ['1728.a1'], 'normalizer': '1.a1', 'old_label': '864.a1', 'projective_image': '46656.ir', 'quotient_action_image': '24.12', 'quotient_action_kernel': '36.9', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '864.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216713496
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '288.c1', '432.l1', '432.t1', '432.ci1'], 'contains': ['1728.d1', '2592.b1', '2592.d1', '2592.e1', '2592.g1', '2592.j1', '2592.j2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316405, 39916800, 31658054504, 37885034880], 'label': '46656.ir.864.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '864.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713497
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '288.d1', '432.b1', '432.f1', '432.k1', '432.m1', '432.p1', '432.u1', '432.cj1'], 'contains': ['1728.e1', '2592.b1', '2592.c1', '2592.g1', '2592.h1', '2592.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 39916800], 'label': '46656.ir.864.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '864.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 216713498
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.a1', '288.b1', '432.g1', '432.q1', '432.v1'], 'contains': ['1728.n1', '2592.c1', '2592.d1', '2592.e1', '2592.i1', '2592.j1', '2592.j2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 325, 1481684504, 39916800], 'label': '46656.ir.864.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '864.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713499
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '288.f1', '432.c1', '432.i1', '432.n1', '432.o1', '432.w1', '432.y1', '432.ck1'], 'contains': ['1728.q1', '2592.b1', '2592.d1', '2592.f1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [325, 39916800, 31658054504, 37885034880], 'label': '46656.ir.864.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '864.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713500
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1', '288.e1', '432.d1', '432.e1', '432.h1', '432.j1', '432.r1', '432.s1', '432.x1'], 'contains': ['1728.s1', '2592.c1', '2592.e1', '2592.f1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 39916800, 104], 'label': '46656.ir.864.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '864.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.f1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713501
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.b1', '288.d1', '288.e1', '432.ba1', '432.bd1', '432.bg1', '432.bk1', '432.bt1', '432.bw1', '432.bz1'], 'contains': ['1728.b1', '2592.c1', '2592.k1', '2592.l1', '2592.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 268280812800, 39916800, 435], 'label': '46656.ir.864.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '864.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713502
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.b1', '288.c1', '288.e1', '432.be1', '432.bx1', '432.ca1'], 'contains': ['1728.c1', '2592.e1', '2592.k1', '2592.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 39916800], 'label': '46656.ir.864.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '864.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713503
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.b1', '288.c1', '288.f1', '432.bq1', '432.cb1', '432.ci1'], 'contains': ['1728.d1', '2592.d1', '2592.k1', '2592.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [268280812800, 325, 1481684504, 39916800], 'label': '46656.ir.864.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.u1', 'old_label': '864.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713504
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.c1', '288.d1', '288.f1', '432.bb1', '432.bl1', '432.bn1', '432.br1', '432.cc1', '432.cj1', '432.cl1'], 'contains': ['1728.e1', '2592.b1', '2592.k1', '2592.m1', '2592.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [268280812800, 39916800, 31658054504, 37885034880], 'label': '46656.ir.864.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '864.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713505
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '12.y1', '12.bc1', '12.cb1'], 'contains': ['48.ce1', '72.hp1', '72.hq1', '72.hr1', '96.bc1', '648.kc1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 622713012218, 41051125, 269279866800], 'label': '46656.ir.24.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '24.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216713506
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1', '288.f1', '432.bc1', '432.bf1', '432.bj1', '432.bs1', '432.by1', '432.cd1', '432.ck1'], 'contains': ['1728.q1', '2592.f1', '2592.k1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 325, 39916800, 355419187304], 'label': '46656.ir.864.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '864.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.k1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713507
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.b1', '288.d1', '432.bh1', '432.bu1', '432.ce1'], 'contains': ['1728.u1', '2592.i1', '2592.l1', '2592.m1', '2592.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 1481684835, 268280812800, 39916800], 'label': '46656.ir.864.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '864.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713508
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.b1', '288.c1', '432.cf1'], 'contains': ['1728.v1', '2592.j1', '2592.m1', '2592.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [40323593624, 268280812800, 39366316405, 39916800], 'label': '46656.ir.864.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.j1', 'old_label': '864.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713509
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.b1', '288.c1', '432.cf2'], 'contains': ['1728.v2', '2592.j2', '2592.m1', '2592.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [268280812800, 39366316405, 39916800, 31658054504], 'label': '46656.ir.864.m2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.q1', 'old_label': '864.m2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.m2', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713510
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.c1', '288.d1', '432.bo1', '432.cg1', '432.cm1'], 'contains': ['1728.w1', '2592.g1', '2592.m1', '2592.n1', '2592.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [268280812800, 1481684504, 39916800, 37885034880], 'label': '46656.ir.864.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.u1', 'old_label': '864.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.n1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713511
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.d1', '432.z1', '432.bi1', '432.bm1', '432.bp1', '432.bv1', '432.ch1', '432.cn1'], 'contains': ['1728.a1', '2592.h1', '2592.l1', '2592.o1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800, 269279866800], 'label': '46656.ir.864.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '864.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.o1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216713512
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.g1', '288.h1', '432.z1', '432.co1', '432.cr1', '432.cs1', '432.ct1', '432.cw1', '432.cx1', '432.cy1', '432.cz1', '432.da1', '432.db1'], 'contains': ['1728.a1', '2592.p1', '2592.q1', '2592.r1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 269279866800], 'label': '46656.ir.864.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.p1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216713513
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.g1', '288.i1', '432.cp1', '432.cq1', '432.cu1', '432.dc1', '432.dd1', '432.de1', '432.df1'], 'contains': ['1728.y1', '2592.r1', '2592.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 7, 655477406640, 269279866800], 'label': '46656.ir.864.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '864.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.q1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713514
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.g1', '288.j1', '432.cv1', '432.dg1', '432.dh1'], 'contains': ['1728.ba1', '2592.r1', '2592.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 7, 269279866800, 623823424560], 'label': '46656.ir.864.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cq1', 'old_label': '864.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.r1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216713515
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.h1', '288.k1', '432.ba1', '432.di1', '432.dj1', '432.do1', '432.dr1', '432.du1', '432.dx1'], 'contains': ['1728.b1', '2592.p1', '2592.u1', '2592.v1', '2592.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [7, 269279866800, 37885034880, 31658054835], 'label': '46656.ir.864.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '864.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713516
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.g1', '12.z1'], 'contains': ['48.cf1', '72.hp1', '72.hr1', '96.bd1', '648.kd1'], 'core': '432.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 463289990028], 'label': '46656.ir.24.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.z1', 'old_label': '24.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1', 'subgroup_fusion': None, 'weyl_group': '3888.bx'}
  • id: 216713517
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.h1', '288.l1', '432.b1', '432.bb1', '432.dk1', '432.dp1', '432.ds1', '432.dt1', '432.dv1'], 'contains': ['1728.e1', '2592.q1', '2592.u1', '2592.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [268280812800, 7, 37885034880, 31658054835], 'label': '46656.ir.864.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '864.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.t1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216713518
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.h1', '288.i1', '288.j1', '288.m1', '432.dl1', '432.dq1', '432.dw1'], 'contains': ['1728.f1', '2592.r1', '2592.v1', '2592.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 7, 269279866800, 104], 'label': '46656.ir.864.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '864.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.u1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713519
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.i1', '288.n1', '432.dm1', '432.dn1', '432.dy1'], 'contains': ['1728.i1', '2592.s1', '2592.v1', '2592.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [387999647280, 7, 93536397441, 387999647384], 'label': '46656.ir.864.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '864.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.v1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713521
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.de1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.k1', '288.l1', '432.c1', '432.bc1', '432.ea1', '432.eg1', '432.ej1', '432.ek1', '432.en1', '432.er1', '432.es1', '432.et1', '432.eu1', '432.ev1', '432.ew1', '432.ex1', '432.ey1'], 'contains': ['1728.q1', '2592.a1', '2592.u1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 325, 31658054504, 37885034880], 'label': '46656.ir.864.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '864.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.x1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713522
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.k1', '288.m1', '288.n1', '288.o1', '432.eb1', '432.eh1', '432.eo1', '432.ez1', '432.fa1', '432.fb1', '432.fc1'], 'contains': ['1728.r1', '2592.a1', '2592.v1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [301891126320, 7, 325, 104], 'label': '46656.ir.864.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '864.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.y1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713523
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.k1', '288.l1', '288.m1', '432.d1', '432.ec1', '432.ed1', '432.ei1', '432.el1', '432.em1', '432.ep1', '432.fd1', '432.fe1', '432.ff1', '432.fg1', '432.fh1', '432.fi1', '432.fj1', '432.fk1'], 'contains': ['1728.s1', '2592.a1', '2592.w1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 7, 325, 104], 'label': '46656.ir.864.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '864.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.z1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713524
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ca1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hm1', '288.n1', '432.ee1', '432.ef1', '432.eq1', '432.fl1', '432.fm1', '432.fn1', '432.fo1'], 'contains': ['1728.t1', '2592.a1', '2592.x1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7, 325, 104, 461482882830], 'label': '46656.ir.864.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '864.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ba1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713525
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.p1', '288.s1', '432.bd1', '432.di1', '432.fs1', '432.ft1', '432.fx1', '432.gb1', '432.hr1'], 'contains': ['1728.b1', '2592.y1', '2592.z1', '2592.ba1', '2592.bf1', '2592.bg1', '2592.bh1', '2592.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827200, 435], 'label': '46656.ir.864.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '864.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713526
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.p1', '288.q1', '432.be1', '432.fy1', '432.gc1'], 'contains': ['1728.c1', '2592.y1', '2592.bc1', '2592.bd1', '2592.bg1', '2592.bj1', '2592.bj2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 39366316405, 6227827200, 382729979624], 'label': '46656.ir.864.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '864.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713527
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '12.ba1', '12.bx1', '12.ca1'], 'contains': ['48.d1', '48.bz1', '48.cc1', '72.hi1', '72.hp1', '216.jx1'], 'core': '48.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.24.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713528
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.p1', '288.t1', '432.gd1'], 'contains': ['1728.g1', '2592.z1', '2592.bb1', '2592.bc1', '2592.bd1', '2592.bh1', '2592.bj1', '2592.bj2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [387999647280, 39366316405, 6227827200, 355419187304], 'label': '46656.ir.864.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ds1', 'old_label': '864.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216713529
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.p1', '288.r1', '432.fu1', '432.ge1', '432.hs1'], 'contains': ['1728.m1', '2592.ba1', '2592.bb1', '2592.bc1', '2592.bi1', '2592.bj1', '2592.bj2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 268280813125, 6227827200, 355419187304], 'label': '46656.ir.864.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '864.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713530
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.eo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1', '288.u1', '432.bf1', '432.ea1', '432.fp1', '432.fw1', '432.fz1', '432.gf1', '432.gi1'], 'contains': ['1728.q1', '2592.y1', '2592.bb1', '2592.be1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 325, 6227827200, 355419187304], 'label': '46656.ir.864.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bf1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713531
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1', '288.w1', '288.x1', '432.eb1', '432.fq1', '432.gg1'], 'contains': ['1728.r1', '2592.z1', '2592.bc1', '2592.be1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [387999647280, 325, 6227827200, 387999647384], 'label': '46656.ir.864.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cf1', 'old_label': '864.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bg1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713532
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1', '288.v1', '432.e1', '432.ec1', '432.fr1', '432.fv1', '432.ga1', '432.gh1', '432.ht1'], 'contains': ['1728.s1', '2592.ba1', '2592.bd1', '2592.be1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 6227827200, 104], 'label': '46656.ir.864.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bh1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713533
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.q1', '288.s1', '288.u1', '432.bg1', '432.dj1', '432.gm1', '432.gt1', '432.gw1', '432.hf1', '432.hr1'], 'contains': ['1728.b1', '2592.y1', '2592.bk1', '2592.bm1', '2592.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [268280812800, 40323593955, 40323593520, 6227827200], 'label': '46656.ir.864.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '864.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713534
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.r1', '288.s1', '288.v1', '432.f1', '432.dk1', '432.gn1', '432.gq1', '432.gz1', '432.hg1', '432.hu1'], 'contains': ['1728.e1', '2592.ba1', '2592.bk1', '2592.bn1', '2592.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 6227827200], 'label': '46656.ir.864.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '864.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713535
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.s1', '288.t1', '288.w1', '288.y1', '432.dl1', '432.go1', '432.hh1'], 'contains': ['1728.f1', '2592.z1', '2592.bk1', '2592.bo1', '2592.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.864.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bb1', 'old_label': '864.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713536
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.x1', '288.y1', '432.dm1', '432.gl1', '432.hc1'], 'contains': ['1728.i1', '2592.z1', '2592.bl1', '2592.bp1', '2592.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [387999647280, 537124538618, 325, 6227827200], 'label': '46656.ir.864.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.de1', 'old_label': '864.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713537
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.r1', '288.t1', '288.u1', '432.gu1', '432.hi1', '432.hs1'], 'contains': ['1728.m1', '2592.bb1', '2592.bk1', '2592.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [294706903784, 381772702405, 40323593520, 6227827200], 'label': '46656.ir.864.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '864.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713538
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['54.l1', '54.m1', '54.n1', '54.bh1', '54.bi1', '54.bj1', '54.bk1', '81.a1', '108.ec1', '243.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39916800, 39957120, 6227827207, 499, 7, 41051125, 174452060430], 'label': '46656.ir.27.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216713539
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.q1', '288.t1', '288.v1', '432.g1', '432.ha1', '432.hj1'], 'contains': ['1728.n1', '2592.bd1', '2592.bk1', '2592.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [325, 1481684504, 40323593520, 6227827200], 'label': '46656.ir.864.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '864.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713540
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.q1', '288.r1', '288.t1', '288.w1', '432.hk1'], 'contains': ['1728.o1', '2592.bc1', '2592.bk1', '2592.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [40323593624, 40323593520, 6227827200, 269279867125], 'label': '46656.ir.864.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '864.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713541
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.x1', '432.hd1'], 'contains': ['1728.p1', '2592.bc1', '2592.bl1', '2592.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [325, 724820544270, 6227827200, 382729979624], 'label': '46656.ir.864.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.eg1', 'old_label': '864.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713542
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.u1', '288.v1', '288.w1', '432.h1', '432.ed1', '432.gk1', '432.gv1', '432.hb1', '432.hl1', '432.ht1'], 'contains': ['1728.s1', '2592.be1', '2592.bk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 6227827200], 'label': '46656.ir.864.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '864.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bq1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713543
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.is1', '288.x1', '432.ee1', '432.gj1', '432.he1'], 'contains': ['1728.t1', '2592.be1', '2592.bl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [325, 6227827200, 104, 461482882830], 'label': '46656.ir.864.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '864.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.br1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713544
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.q1', '288.s1', '432.bh1', '432.gx1', '432.hm1'], 'contains': ['1728.u1', '2592.bg1', '2592.bm1', '2592.br1', '2592.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [268280812800, 1481684504, 40323593520, 6227827200], 'label': '46656.ir.864.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '864.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713545
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.r1', '288.s1', '432.gr1', '432.hn1', '432.hv1'], 'contains': ['1728.w1', '2592.bi1', '2592.bn1', '2592.bq1', '2592.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 270715783064, 1481684400, 6227827200], 'label': '46656.ir.864.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '864.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713546
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.s1', '288.z1', '432.bi1', '432.co1', '432.gp1', '432.gs1', '432.gy1', '432.ho1', '432.hw1'], 'contains': ['1728.a1', '2592.bf1', '2592.bm1', '2592.bn1', '2592.bo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.864.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '864.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713547
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.s1', '288.t1', '288.ba1', '432.hp1'], 'contains': ['1728.x1', '2592.bh1', '2592.bo1', '2592.bq1', '2592.br1', '2592.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1481684504, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.864.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '864.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713548
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.q1', '288.r1', '288.t1', '432.hq1'], 'contains': ['1728.bh1', '2592.bj1', '2592.bq1', '2592.br1', '2592.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [381772702405, 40323593520, 6227827200, 382729979624], 'label': '46656.ir.864.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '864.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713549
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.d1', '12.e1', '12.f1', '12.g1', '12.j1', '12.bd1', '12.be1', '12.bf1', '12.bg1', '12.bl1', '12.bm1', '18.a1', '18.e1', '54.f1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 1174645, 1174320, 6227827207, 499, 7, 269279866800], 'label': '46656.ir.6.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713550
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['54.b1', '54.c1', '54.d1', '54.e1', '54.j1', '54.k1', '54.o1', '54.p1', '54.q1', '54.r1', '54.s1', '54.bf1', '54.bg1', '54.bl1', '54.bm1', '81.a1', '243.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39916800, 39957120, 268280812800, 6227827207, 499, 7, 41051125], 'label': '46656.ir.27.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '27.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216713551
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.q1', '288.r1', '288.t1', '432.hq2'], 'contains': ['1728.bh2', '2592.bj2', '2592.bq1', '2592.br1', '2592.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [40323593520, 6227827200, 382729979624, 269279867125], 'label': '46656.ir.864.bw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '864.bw2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bw2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713552
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ez1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.y1', '288.z1', '288.ba1', '432.cp1', '432.hx1', '432.hy1'], 'contains': ['1728.y1', '2592.bo1', '2592.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [624302466480, 270715782960, 40323593520, 6227827200], 'label': '46656.ir.864.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '864.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bx1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713553
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cg1', '288.bb1', '432.ef1', '432.gj1', '432.hz1'], 'contains': ['1728.t1', '2592.bu1', '2592.bv1', '2592.bw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 325, 174452060430, 104], 'label': '46656.ir.864.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '864.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.by1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713554
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bb1', '288.bc1', '432.dn1', '432.gl1', '432.id1'], 'contains': ['1728.i1', '2592.bu1', '2592.by1', '2592.ca1', '2592.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [41091120, 387999647280, 93536397441, 387999647384], 'label': '46656.ir.864.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.de1', 'old_label': '864.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713555
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bb1', '288.bd1', '432.ie1'], 'contains': ['1728.j1', '2592.bv1', '2592.by1', '2592.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [41091120, 174564190515, 301891126320, 104], 'label': '46656.ir.864.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ex1', 'old_label': '864.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713556
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.be1', '288.bf1', '432.i1', '432.bj1', '432.eg1', '432.fp1', '432.ia1', '432.ic1', '432.if1'], 'contains': ['1728.q1', '2592.bw1', '2592.bx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 325, 31658054504, 37885034880], 'label': '46656.ir.864.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '864.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cb1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713557
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bb1', '288.be1', '288.bg1', '432.eh1', '432.fq1', '432.ig1'], 'contains': ['1728.r1', '2592.bw1', '2592.by1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 301891126320, 325, 104], 'label': '46656.ir.864.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '864.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cc1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713558
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.be1', '288.bf1', '288.bg1', '432.j1', '432.ei1', '432.fr1', '432.gk1', '432.ib1', '432.ih1', '432.ii1'], 'contains': ['1728.s1', '2592.bw1', '2592.bz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 104], 'label': '46656.ir.864.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '864.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cd1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713559
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.be1', '288.bh1', '432.bk1', '432.do1', '432.fs1', '432.gm1', '432.ik1', '432.im1', '432.in1'], 'contains': ['1728.b1', '2592.bx1', '2592.by1', '2592.bz1', '2592.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41091120, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.864.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '864.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713560
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bf1', '288.bh1', '432.k1', '432.bl1', '432.dp1', '432.gn1', '432.ij1', '432.il1', '432.io1'], 'contains': ['1728.e1', '2592.bx1', '2592.bz1', '2592.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 268280812800, 37885034880, 31658054835], 'label': '46656.ir.864.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '864.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cf1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713561
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '9.b1'], 'contains': ['54.f1', '54.g1', '54.h1', '54.i1', '54.t1', '54.u1', '54.v1', '54.w1', '54.y1', '54.z1', '54.ba1', '54.bb1', '54.bc1', '54.bd1', '54.be1', '81.b1', '243.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 499, 1521641964, 269279866800, 443609999724], 'label': '46656.ir.27.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '27.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713562
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bc1', '288.bd1', '288.bg1', '288.bh1', '432.dq1', '432.go1', '432.ip1'], 'contains': ['1728.f1', '2592.by1', '2592.bz1', '2592.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [41091120, 39366316080, 269279866800, 435], 'label': '46656.ir.864.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1', 'old_label': '864.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cg1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216713563
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bc1', '288.bi1', '432.cq1', '432.hx1', '432.iq1'], 'contains': ['1728.y1', '2592.ca1', '2592.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091120, 39366316080, 655477406640, 269279866800], 'label': '46656.ir.864.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '864.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ch1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713564
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bc1', '288.bd1', '288.bj1', '432.ir1'], 'contains': ['1728.z1', '2592.cb1', '2592.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [41091120, 39366316080, 270715782960, 195089010864], 'label': '46656.ir.864.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bp1', 'old_label': '864.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ci1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713565
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '288.bl1', '432.y1', '432.bj1', '432.ej1', '432.gi1', '432.iu1', '432.iv1', '432.iw1', '432.ix1', '432.iy1', '432.iz1', '432.ja1', '432.jb1', '432.jc1', '432.jd1', '432.jx1'], 'contains': ['1728.q1', '2592.cf1', '2592.cg1', '2592.ch1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 325, 1481684400, 1521641624], 'label': '46656.ir.864.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '864.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cj1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713566
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bk1', '288.bn1', '432.bk1', '432.dr1', '432.hr1', '432.jf1', '432.jg1', '432.jo1', '432.jt1'], 'contains': ['1728.b1', '2592.cf1', '2592.cj1', '2592.ck1', '2592.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [301891126320, 39957120, 1481684400, 1521641624], 'label': '46656.ir.864.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '864.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ck1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713567
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bl1', '288.bm1', '432.ci1', '432.jh1', '432.jq1'], 'contains': ['1728.d1', '2592.cg1', '2592.ci1', '2592.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39957120, 325, 37885034880, 1521641624], 'label': '46656.ir.864.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '864.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713568
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bl1', '288.bn1', '432.bl1', '432.cj1', '432.ds1', '432.ji1', '432.jm1', '432.jr1', '432.kx1'], 'contains': ['1728.e1', '2592.cf1', '2592.ci1', '2592.cl1', '2592.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 1481684400], 'label': '46656.ir.864.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bn1', 'old_label': '864.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713569
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bk1', '288.bm1', '432.hs1', '432.jj1', '432.ju1'], 'contains': ['1728.m1', '2592.cg1', '2592.cj1', '2592.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684725, 387037284480, 39957120, 39957224], 'label': '46656.ir.864.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '864.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713570
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bl1', '288.bo1', '432.i1', '432.ck1', '432.ek1', '432.jk1', '432.jn1', '432.js1', '432.jx1'], 'contains': ['1728.q1', '2592.ch1', '2592.ci1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 325, 31697930984, 37885034880], 'label': '46656.ir.864.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '864.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.co1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713571
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bk1', '288.bo1', '432.j1', '432.el1', '432.ht1', '432.je1', '432.jl1', '432.jp1', '432.jv1'], 'contains': ['1728.s1', '2592.ch1', '2592.cj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [387037284480, 39957120, 325, 39957224], 'label': '46656.ir.864.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cp1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713572
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '16.b1', '16.c1', '16.d1', '16.e1', '16.f1', '16.g1', '16.h1'], 'contains': ['64.a1', '96.a1', '96.e1', '96.f1', '96.g1'], 'core': '96.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 461482882830], 'label': '46656.ir.32.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '32.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216713573
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bm1', '288.bn1', '288.bo1', '432.k1', '432.cl1', '432.dt1', '432.hu1', '432.jy1', '432.ka1', '432.ke1', '432.kg1', '432.kh1', '432.kk1', '432.kn1', '432.ko1', '432.kp1', '432.kq1', '432.kx1'], 'contains': ['1728.e1', '2592.ci1', '2592.cj1', '2592.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [268280812800, 39957120, 31697930984, 37885034880], 'label': '46656.ir.864.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '864.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cq1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713574
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bm1', '288.bn1', '432.cm1', '432.hv1', '432.kb1', '432.ki1', '432.kl1', '432.kr1', '432.ks1'], 'contains': ['1728.w1', '2592.cl1', '2592.cn1', '2592.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1521641955, 268280812800, 39957120, 37885034880], 'label': '46656.ir.864.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '864.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cr1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713575
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.er1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bn1', '432.a1', '432.bm1', '432.cn1', '432.cs1', '432.hw1', '432.jz1', '432.kc1', '432.kd1', '432.kf1', '432.kj1', '432.km1', '432.kt1', '432.ku1', '432.kv1', '432.kw1'], 'contains': ['1728.a1', '2592.ck1', '2592.cm1', '2592.co1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 269279866800], 'label': '46656.ir.864.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '864.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cs1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713576
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bp1', '288.bq1', '288.br1', '432.e1', '432.em1', '432.gk1', '432.je1', '432.ky1', '432.kz1', '432.la1'], 'contains': ['1728.s1', '2592.cp1', '2592.cq1', '2592.cr1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 325, 104, 6267744000], 'label': '46656.ir.864.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '864.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ct1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713577
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bp1', '288.bt1', '432.bd1', '432.du1', '432.gm1', '432.jf1', '432.lc1', '432.lf1', '432.lp1'], 'contains': ['1728.b1', '2592.cp1', '2592.cs1', '2592.cw1', '2592.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 268280812800, 104, 6267744000], 'label': '46656.ir.864.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '864.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713578
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bp1', '288.bs1', '432.be1', '432.lg1', '432.lq1'], 'contains': ['1728.c1', '2592.cq1', '2592.cs1', '2592.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 39366316405, 382729979624, 6267744000], 'label': '46656.ir.864.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '864.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713579
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bq1', '288.bt1', '432.f1', '432.dv1', '432.gn1', '432.jy1', '432.lb1', '432.lh1', '432.ls1'], 'contains': ['1728.e1', '2592.cp1', '2592.cu1', '2592.cy1', '2592.db1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 6267744000], 'label': '46656.ir.864.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '864.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713580
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.br1', '288.bt1', '288.bu1', '288.bv1', '432.dw1', '432.go1', '432.li1'], 'contains': ['1728.f1', '2592.cp1', '2592.ct1', '2592.cz1', '2592.da1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 269279866800, 104, 6267744000], 'label': '46656.ir.864.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.dh1', 'old_label': '864.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713581
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.br1', '288.bs1', '288.bw1', '288.bx1', '432.lj1'], 'contains': ['1728.h1', '2592.cq1', '2592.ct1', '2592.da1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [269279866904, 301891126320, 325, 6267744000], 'label': '46656.ir.864.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.gy1', 'old_label': '864.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713582
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bq1', '288.bs1', '432.g1', '432.lk1', '432.lt1'], 'contains': ['1728.n1', '2592.cq1', '2592.cu1', '2592.db1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [325, 1481684504, 40323593520, 6267744000], 'label': '46656.ir.864.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '864.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.cz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713583
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '16.b1', '16.i1', '16.j1'], 'contains': ['64.a1', '96.h1', '96.i1', '96.j1', '96.k1'], 'core': '192.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827200, 461482882830], 'label': '46656.ir.32.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '32.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216713584
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ht1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bp1', '288.by1', '432.bf1', '432.en1', '432.fp1', '432.iu1', '432.le1', '432.ll1', '432.lr1'], 'contains': ['1728.q1', '2592.cr1', '2592.cs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 325, 355419187304, 6267744000], 'label': '46656.ir.864.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.da1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713585
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.br1', '288.by1', '288.bz1', '288.ca1', '432.eo1', '432.fq1', '432.lm1'], 'contains': ['1728.r1', '2592.cr1', '2592.ct1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [301891126320, 325, 104, 6267744000], 'label': '46656.ir.864.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '864.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.db1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713586
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bq1', '288.by1', '432.h1', '432.ep1', '432.fr1', '432.je1', '432.ld1', '432.ln1', '432.lu1'], 'contains': ['1728.s1', '2592.cr1', '2592.cu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 6267744000], 'label': '46656.ir.864.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '864.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dc1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713587
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jp1', '288.bz1', '432.eq1', '432.gj1', '432.lo1'], 'contains': ['1728.t1', '2592.cr1', '2592.cv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [325, 174451657230, 104, 6267744000], 'label': '46656.ir.864.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '864.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dd1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216713588
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bs1', '288.bt1', '288.by1', '432.bg1', '432.dx1', '432.fs1', '432.jf1', '432.lw1', '432.lx1', '432.md1'], 'contains': ['1728.b1', '2592.cs1', '2592.ct1', '2592.cu1', '2592.dc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [268280812800, 40323593955, 40323593520, 6267744000], 'label': '46656.ir.864.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '864.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.de1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713589
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bu1', '288.bw1', '288.bz1', '432.dy1', '432.gl1', '432.ma1'], 'contains': ['1728.i1', '2592.ct1', '2592.cv1', '2592.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [555805963521, 294706903784, 388956924720, 6267744000], 'label': '46656.ir.864.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1', 'old_label': '864.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.df1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216713590
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bv1', '288.bx1', '288.ca1', '432.dz1'], 'contains': ['1728.k1', '2592.ct1', '2592.de1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [568299881978, 325, 388956924720, 6267744000], 'label': '46656.ir.864.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1', 'old_label': '864.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dg1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 216713591
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bs1', '288.bt1', '432.bh1', '432.ly1', '432.me1'], 'contains': ['1728.u1', '2592.cx1', '2592.da1', '2592.db1', '2592.dc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684835, 268280812800, 40323593520, 6267744000], 'label': '46656.ir.864.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '864.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713592
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bt1', '288.cb1', '432.bi1', '432.ct1', '432.gp1', '432.jz1', '432.lv1', '432.lz1', '432.mf1'], 'contains': ['1728.a1', '2592.cw1', '2592.cy1', '2592.cz1', '2592.dc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 6267744000], 'label': '46656.ir.864.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '864.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.di1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713593
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bu1', '288.cb1', '432.cu1', '432.hx1', '432.mb1'], 'contains': ['1728.y1', '2592.cz1', '2592.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 655477406640, 269279866800, 6267744000], 'label': '46656.ir.864.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '864.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dj1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713594
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '16.c1', '16.i1', '16.k1'], 'contains': ['64.a1', '96.b1', '96.l1', '96.m1', '96.n1'], 'core': '96.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 269279866800, 461482882830], 'label': '46656.ir.32.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '32.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '1296.838'}
  • id: 216713595
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bv1', '288.cb1', '432.cv1'], 'contains': ['1728.ba1', '2592.cz1', '2592.de1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 269279866800, 623823424560, 6267744000], 'label': '46656.ir.864.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '864.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dk1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216713596
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bu1', '288.bw1', '432.mc1'], 'contains': ['1728.bd1', '2592.da1', '2592.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [270715783064, 623711294721, 388956924720, 6267744000], 'label': '46656.ir.864.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.ci1', 'old_label': '864.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dl1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713597
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bv1', '288.bx1'], 'contains': ['1728.bf1', '2592.da1', '2592.de1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [622713012218, 388956924720, 34096648645, 6267744000], 'label': '46656.ir.864.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.r1', 'old_label': '864.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dm1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216713598
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '288.cd1', '288.ce1', '432.b1', '432.bn1', '432.gq1', '432.ij1', '432.jm1', '432.ka1', '432.lb1'], 'contains': ['1728.e1', '2592.df1', '2592.dg1', '2592.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684835, 1481684400], 'label': '46656.ir.864.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '864.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dn1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216713599
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '288.cd1', '432.bo1', '432.gr1', '432.kb1'], 'contains': ['1728.w1', '2592.df1', '2592.dj1', '2592.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 270715783395], 'label': '46656.ir.864.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '864.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.do1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216713600
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.do1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cd1', '432.z1', '432.bp1', '432.gs1', '432.is1', '432.kc1', '432.kd1', '432.lv1'], 'contains': ['1728.a1', '2592.df1', '2592.di1', '2592.dk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 269279866800], 'label': '46656.ir.864.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '864.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dp1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
  • id: 216713601
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cd1', '288.cf1', '432.ba1', '432.ft1', '432.gt1', '432.ik1', '432.jg1', '432.lc1', '432.lw1'], 'contains': ['1728.b1', '2592.dh1', '2592.di1', '2592.dl1', '2592.dm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 104], 'label': '46656.ir.864.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '864.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dq1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713602
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '288.cg1', '432.l1', '432.bq1', '432.jh1'], 'contains': ['1728.d1', '2592.dg1', '2592.dj1', '2592.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39916807, 293708217925, 355419187304, 37885034880], 'label': '46656.ir.864.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '864.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dr1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713603
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cd1', '288.cg1', '432.m1', '432.bb1', '432.br1', '432.il1', '432.ji1', '432.jm1', '432.ke1'], 'contains': ['1728.e1', '2592.dg1', '2592.dj1', '2592.dk1', '2592.dm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 268280812800, 31658054504, 37885034880], 'label': '46656.ir.864.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.br1', 'old_label': '864.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ds1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713604
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cc1', '288.cf1', '432.fu1', '432.gu1', '432.jj1'], 'contains': ['1728.m1', '2592.dh1', '2592.dl1', '2592.dn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39916807, 39366316080, 268280813125, 355419187304], 'label': '46656.ir.864.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fz1', 'old_label': '864.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dt1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713605
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '16.d1', '16.i1', '16.l1'], 'contains': ['64.a1', '96.p1', '96.q1', '96.r1', '96.s1'], 'core': '192.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 455255499150, 325, 1481684400, 1481684504, 269279866800, 6267744000], 'label': '46656.ir.32.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '32.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '1296.838'}
  • id: 216713606
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ce1', '288.cg1', '432.c1', '432.n1', '432.bs1', '432.ia1', '432.iv1', '432.jk1', '432.jn1'], 'contains': ['1728.q1', '2592.dg1', '2592.do1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 325, 31658054504, 37885034880], 'label': '46656.ir.864.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '864.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.du1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713607
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ce1', '288.cf1', '432.d1', '432.fv1', '432.gv1', '432.ib1', '432.jl1', '432.ky1', '432.ld1'], 'contains': ['1728.s1', '2592.dh1', '2592.do1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 104], 'label': '46656.ir.864.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '864.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dv1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713608
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '288.cg1', '432.o1', '432.bc1', '432.fw1', '432.ic1', '432.iw1', '432.jn1', '432.le1'], 'contains': ['1728.q1', '2592.dm1', '2592.dn1', '2592.do1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 268280812800, 325, 355419187304], 'label': '46656.ir.864.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '864.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713609
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '288.ci1', '288.cj1', '432.bt1', '432.di1', '432.gw1', '432.im1', '432.jo1', '432.lc1', '432.lx1'], 'contains': ['1728.b1', '2592.dp1', '2592.dq1', '2592.dr1', '2592.ds1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827207, 435], 'label': '46656.ir.864.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '864.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713610
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '288.ci1', '432.bu1', '432.gx1', '432.ly1'], 'contains': ['1728.u1', '2592.dp1', '2592.du1', '2592.dx1', '2592.ea1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 268280812800, 1481684504, 6227827207], 'label': '46656.ir.864.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '864.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713611
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ci1', '288.ck1', '288.cl1', '432.bv1', '432.co1', '432.gy1', '432.it1', '432.kf1', '432.lv1', '432.lz1'], 'contains': ['1728.a1', '2592.dp1', '2592.dt1', '2592.dv1', '2592.dw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.864.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '864.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.dz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713612
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ci1', '288.cp1', '432.bw1', '432.dj1', '432.fx1', '432.in1', '432.jo1', '432.lf1', '432.lw1'], 'contains': ['1728.b1', '2592.dq1', '2592.dt1', '2592.du1', '2592.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 268280812800, 40323593520, 6227827207], 'label': '46656.ir.864.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '864.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ea1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713613
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '288.cp1', '432.bx1', '432.fy1', '432.lg1'], 'contains': ['1728.c1', '2592.dq1', '2592.du1', '2592.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 301891126645, 355419187304, 6227827207], 'label': '46656.ir.864.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '864.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eb1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713614
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ci1', '288.cq1', '432.p1', '432.dk1', '432.gz1', '432.io1', '432.kg1', '432.lb1', '432.lh1'], 'contains': ['1728.e1', '2592.ds1', '2592.dv1', '2592.ea1', '2592.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 6227827207], 'label': '46656.ir.864.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '864.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ec1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713615
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ci1', '288.cm1', '288.cn1', '288.cr1', '432.dl1', '432.ip1', '432.li1'], 'contains': ['1728.f1', '2592.dr1', '2592.dw1', '2592.dx1', '2592.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593955, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.864.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cs1', 'old_label': '864.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ed1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713616
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '16.b1', '16.k1', '16.l1'], 'contains': ['64.a1', '96.u1', '96.v1', '96.w1', '96.x1'], 'core': '192.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207, 461482882830], 'label': '46656.ir.32.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '32.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216713617
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '288.co1', '288.cr1', '432.lj1'], 'contains': ['1728.h1', '2592.dr1', '2592.dx1', '2592.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [299935198184, 387999647280, 6227827207, 269279867125], 'label': '46656.ir.864.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hd1', 'old_label': '864.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ee1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713618
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cm1', '288.co1', '288.cs1', '432.dm1', '432.id1', '432.ma1'], 'contains': ['1728.i1', '2592.dr1', '2592.dy1', '2592.dz1', '2592.ed1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387999647280, 93536397441, 6227827207, 387999647384], 'label': '46656.ir.864.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '864.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ef1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713619
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cn1', '288.co1', '288.cs1', '432.ie1'], 'contains': ['1728.j1', '2592.dr1', '2592.dz1', '2592.ee1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [387999647280, 455107081395, 6227827207, 387999647384], 'label': '46656.ir.864.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ie1', 'old_label': '864.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eg1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713620
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '288.cq1', '432.q1', '432.ha1', '432.lk1'], 'contains': ['1728.n1', '2592.ds1', '2592.ea1', '2592.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 325, 1481684504, 6227827207], 'label': '46656.ir.864.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '864.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eh1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713621
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cj1', '288.cp1', '432.by1', '432.ea1', '432.fz1', '432.if1', '432.ix1', '432.le1', '432.ll1'], 'contains': ['1728.q1', '2592.dq1', '2592.ef1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 325, 355419187304, 6227827207], 'label': '46656.ir.864.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ei1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713622
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cj1', '288.cr1', '288.cs1', '432.eb1', '432.ig1', '432.lm1'], 'contains': ['1728.r1', '2592.dr1', '2592.ef1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [387999647280, 325, 6227827207, 387999647384], 'label': '46656.ir.864.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cf1', 'old_label': '864.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ej1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713623
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cj1', '288.cq1', '432.r1', '432.ec1', '432.hb1', '432.ih1', '432.jp1', '432.ky1', '432.ln1'], 'contains': ['1728.s1', '2592.ds1', '2592.ef1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 6227827207, 104], 'label': '46656.ir.864.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ek1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713624
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ck1', '288.cm1', '432.cp1', '432.iq1', '432.mb1'], 'contains': ['1728.y1', '2592.dw1', '2592.dy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [624302466480, 270715782960, 40323593520, 6227827207], 'label': '46656.ir.864.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '864.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.el1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713625
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cl1', '288.cm1', '288.cn1', '432.ir1'], 'contains': ['1728.z1', '2592.dw1', '2592.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [40323593520, 269279866800, 6227827207, 463289990028], 'label': '46656.ir.864.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fk1', 'old_label': '864.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.em1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713626
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cm1', '288.co1', '432.mc1'], 'contains': ['1728.bd1', '2592.dx1', '2592.dy1', '2592.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [40323593624, 387999647280, 93536397441, 6227827207], 'label': '46656.ir.864.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.mc1', 'old_label': '864.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.en1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713627
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '16.c1', '16.j1', '16.l1'], 'contains': ['64.a1', '96.c1', '96.z1', '96.ba1', '96.bb1'], 'core': '96.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 461482882830, 41091127], 'label': '46656.ir.32.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '32.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216713628
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cn1', '288.co1'], 'contains': ['1728.be1', '2592.dx1', '2592.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [387999647280, 6227827207, 463289990028, 269279867125], 'label': '46656.ir.864.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.eo1', 'old_label': '864.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eo1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713629
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cp1', '288.cq1', '288.cr1', '432.s1', '432.ed1', '432.ga1', '432.ii1', '432.jp1', '432.kz1', '432.ld1'], 'contains': ['1728.s1', '2592.eb1', '2592.ec1', '2592.ef1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 6227827207], 'label': '46656.ir.864.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '864.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ep1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713630
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.js1', '288.cs1', '432.ee1', '432.hz1', '432.lo1'], 'contains': ['1728.t1', '2592.ed1', '2592.ee1', '2592.ef1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [325, 6227827207, 104, 461482882830], 'label': '46656.ir.864.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '864.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eq1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713631
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ct1', '288.cv1', '288.cw1', '432.bz1', '432.dr1', '432.fx1', '432.gw1', '432.ik1', '432.lp1', '432.md1'], 'contains': ['1728.b1', '2592.eg1', '2592.eh1', '2592.ej1', '2592.em1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1481684835, 301891126320, 1481684400, 39957127], 'label': '46656.ir.864.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '864.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.er1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713632
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ct1', '288.cu1', '288.cw1', '432.ca1', '432.fy1', '432.lq1'], 'contains': ['1728.c1', '2592.eg1', '2592.ej1', '2592.eo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [293708217925, 1481684400, 1481684504, 39957127], 'label': '46656.ir.864.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '864.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.es1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713633
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ct1', '288.cu1', '288.cx1', '432.l1', '432.cb1', '432.jq1'], 'contains': ['1728.d1', '2592.eg1', '2592.ei1', '2592.en1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316405, 1481684400, 31658054504, 39957127], 'label': '46656.ir.864.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '864.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.et1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713634
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cu1', '288.cv1', '288.cx1', '432.m1', '432.bn1', '432.cc1', '432.ds1', '432.il1', '432.jr1', '432.kh1'], 'contains': ['1728.e1', '2592.eg1', '2592.ei1', '2592.ek1', '2592.el1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 39957127], 'label': '46656.ir.864.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '864.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.eu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713635
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cw1', '288.cx1', '432.n1', '432.cd1', '432.ej1', '432.fz1', '432.ic1', '432.js1', '432.lr1', '432.mg1', '432.mh1'], 'contains': ['1728.q1', '2592.eg1', '2592.ep1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [325, 1481684400, 1481684504, 39957127], 'label': '46656.ir.864.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '864.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ev1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713636
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ct1', '288.cv1', '432.ce1', '432.gx1', '432.me1'], 'contains': ['1728.u1', '2592.eh1', '2592.ei1', '2592.ej1', '2592.es1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [301891126320, 1481684400, 39957127, 31658054835], 'label': '46656.ir.864.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '864.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ew1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713637
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ct1', '288.cu1', '432.cf1'], 'contains': ['1728.v1', '2592.ei1', '2592.ej1', '2592.et1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [39366316405, 1481684400, 382729979624, 39957127], 'label': '46656.ir.864.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.cf1', 'old_label': '864.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ex1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713638
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '16.d1', '16.j1', '16.k1'], 'contains': ['64.a1', '96.bc1', '96.bd1', '96.be1', '96.bf1', '96.bg1', '96.bh1', '96.bi1'], 'core': '192.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6267744007, 39366316080, 455255499150, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.32.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '32.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216713639
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ex2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ct1', '288.cu1', '432.cf2', '432.mi1', '432.mj1'], 'contains': ['1728.v2', '2592.ei1', '2592.ej1', '2592.et2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316405, 1481684400, 39957127, 387999647384], 'label': '46656.ir.864.ex2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '864.ex2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ex2', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713640
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cu1', '288.cv1', '432.bo1', '432.cg1', '432.ki1'], 'contains': ['1728.w1', '2592.ei1', '2592.ej1', '2592.ek1', '2592.eq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 270715783064, 1481684400, 39957127], 'label': '46656.ir.864.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.di1', 'old_label': '864.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ey1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713641
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cv1', '432.bp1', '432.ch1', '432.cs1', '432.gy1', '432.is1', '432.kj1', '432.mf1', '432.mk1', '432.ml1'], 'contains': ['1728.a1', '2592.eh1', '2592.ek1', '2592.er1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 39957127], 'label': '46656.ir.864.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '864.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ez1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216713642
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cu1', '288.cy1', '432.t1', '432.bq1', '432.jq1'], 'contains': ['1728.d1', '2592.el1', '2592.en1', '2592.eo1', '2592.eq1', '2592.et1', '2592.et2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [293708217925, 355419187304, 39957127, 37885034880], 'label': '46656.ir.864.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '864.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fa1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713643
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cv1', '288.cy1', '432.u1', '432.br1', '432.dt1', '432.gz1', '432.ij1', '432.jr1', '432.ls1'], 'contains': ['1728.e1', '2592.el1', '2592.em1', '2592.eq1', '2592.er1', '2592.es1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [268280812800, 31658054504, 39957127, 37885034880], 'label': '46656.ir.864.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '864.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713644
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ct1', '288.cy1', '432.v1', '432.ha1', '432.lt1'], 'contains': ['1728.n1', '2592.em1', '2592.en1', '2592.eo1', '2592.es1', '2592.et1', '2592.et2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [387037284480, 325, 355419187304, 39957127], 'label': '46656.ir.864.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '864.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fc1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713645
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cx1', '288.cy1', '432.o1', '432.w1', '432.bs1', '432.ek1', '432.ia1', '432.iy1', '432.js1'], 'contains': ['1728.q1', '2592.el1', '2592.en1', '2592.ep1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [325, 31658054504, 39957127, 37885034880], 'label': '46656.ir.864.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '864.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fd1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713646
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cw1', '288.cy1', '432.x1', '432.el1', '432.ga1', '432.hb1', '432.ib1', '432.la1', '432.lu1'], 'contains': ['1728.s1', '2592.em1', '2592.eo1', '2592.ep1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [387037284480, 325, 39957127, 104], 'label': '46656.ir.864.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fe1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713647
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cz1', '288.da1', '288.db1', '432.dn1', '432.hc1', '432.ma1'], 'contains': ['1728.i1', '2592.eu1', '2592.ev1', '2592.ew1', '2592.ey1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387999647280, 93536397441, 387999647384, 41091127], 'label': '46656.ir.864.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '864.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ff1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713648
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.db1', '432.hd1'], 'contains': ['1728.p1', '2592.eu1', '2592.ew1', '2592.fb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [300933849205, 174452060430, 382729979624, 41091127], 'label': '46656.ir.864.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hd1', 'old_label': '864.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fg1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713649
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['1296.lv1', '1296.lz1', '1296.ff1', '1296.fc1', '1296.lu1', '1296.ly1', '1296.a1', '1296.fd1', '1296.fb1', '1296.fe1'], 'conjugacy_class_count': 1, 'contained_in': ['12.x1', '18.m1'], 'contains': ['72.a1', '72.b1', '72.c1', '108.cp1', '144.et1', '972.bm1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 6227827200, 623823424560], 'label': '46656.ir.36.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['72.a1', '72.b1', '72.c1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '46656.ir', 'quotient_action_image': '4.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216713650
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jr1', '288.db1', '432.ef1', '432.he1', '432.lo1'], 'contains': ['1728.t1', '2592.eu1', '2592.fd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [325, 174452060430, 104, 41091127], 'label': '46656.ir.864.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '864.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fh1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713651
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cz1', '288.dc1', '288.dd1', '432.cq1', '432.hy1', '432.mb1'], 'contains': ['1728.y1', '2592.ev1', '2592.fi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 655477406640, 269279866800, 41091127], 'label': '46656.ir.864.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '864.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fi1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713652
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cz1', '288.da1', '432.mc1'], 'contains': ['1728.bd1', '2592.ev1', '2592.fk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [40323593624, 387999647280, 132379435521, 41091127], 'label': '46656.ir.864.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.mc1', 'old_label': '864.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fj1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713653
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.dg1', '288.di1', '432.bz1', '432.do1', '432.gb1', '432.hf1', '432.jg1', '432.lf1', '432.lx1'], 'contains': ['1728.b1', '2592.ex1', '2592.ey1', '2592.ez1', '2592.fe1', '2592.fg1', '2592.fj1', '2592.fl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [269279866800, 37885034880, 41091127, 31658054835], 'label': '46656.ir.864.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '864.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fk1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713654
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.df1', '288.di1', '432.ca1', '432.gc1', '432.lg1'], 'contains': ['1728.c1', '2592.ex1', '2592.fb1', '2592.fc1', '2592.fg1', '2592.fo1', '2592.fo2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [270715783064, 325, 37885034880, 41091127], 'label': '46656.ir.864.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '864.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fl1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713655
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.df1', '288.dj1', '432.t1', '432.cb1', '432.jh1'], 'contains': ['1728.d1', '2592.ex1', '2592.fa1', '2592.fc1', '2592.ff1', '2592.fp1', '2592.fp2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387037284805, 299935198184, 37885034880, 41091127], 'label': '46656.ir.864.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '864.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fm1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713656
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.df1', '288.dg1', '288.dj1', '432.u1', '432.cc1', '432.dp1', '432.hg1', '432.ji1', '432.ka1', '432.lh1'], 'contains': ['1728.e1', '2592.ex1', '2592.ez1', '2592.ff1', '2592.fh1', '2592.fm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 31658054504, 37885034880, 41091127], 'label': '46656.ir.864.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '864.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713657
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.cz1', '288.dg1', '288.dh1', '288.dk1', '432.dq1', '432.hh1', '432.li1'], 'contains': ['1728.f1', '2592.ey1', '2592.ez1', '2592.fi1', '2592.fk1', '2592.fn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 269279866800, 41091127, 435], 'label': '46656.ir.864.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '864.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fo1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216713658
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.dh1', '288.di1', '432.gd1'], 'contains': ['1728.g1', '2592.ey1', '2592.fa1', '2592.fb1', '2592.fc1', '2592.fj1', '2592.fo1', '2592.fo2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [301891126320, 268280812904, 355419187525, 41091127], 'label': '46656.ir.864.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.gd1', 'old_label': '864.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fp1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 216713659
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.da1', '288.de1', '288.dk1', '432.lj1'], 'contains': ['1728.h1', '2592.ey1', '2592.fc1', '2592.fk1', '2592.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [269279866904, 301891126320, 325, 41091127], 'label': '46656.ir.864.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.hh1', 'old_label': '864.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fq1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216713660
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.f1', '12.i1', '12.k1', '12.bh1', '12.bi1', '12.bn1', '12.bo1', '18.b1', '54.g1', '54.k1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 1174645, 1174320, 6227827207, 7, 39957619, 269279866800], 'label': '46656.ir.6.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713661
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '18.a1'], 'contains': ['72.d1', '72.f1', '72.h1', '72.dm1', '72.dn1', '72.fh1', '72.fi1', '108.c1', '108.e1', '324.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 6227827207, 499, 7, 325], 'label': '46656.ir.36.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216713662
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.df1', '288.dh1', '288.di1', '432.ge1', '432.hi1', '432.jj1'], 'contains': ['1728.m1', '2592.ez1', '2592.fa1', '2592.fb1', '2592.fl1', '2592.fo1', '2592.fo2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 325, 355419187304, 41091127], 'label': '46656.ir.864.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '864.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fr1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713663
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.dh1', '288.dj1', '432.v1', '432.hj1', '432.lk1'], 'contains': ['1728.n1', '2592.ez1', '2592.fa1', '2592.fc1', '2592.fm1', '2592.fp1', '2592.fp2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 325, 1481684504, 41091127], 'label': '46656.ir.864.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '864.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fs1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713664
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.df1', '288.dh1', '288.dk1', '432.hk1'], 'contains': ['1728.o1', '2592.ez1', '2592.fb1', '2592.fc1', '2592.fn1', '2592.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [39366316080, 270715783064, 325, 41091127], 'label': '46656.ir.864.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hk1', 'old_label': '864.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ft1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713665
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.di1', '288.dj1', '432.w1', '432.cd1', '432.eg1', '432.gf1', '432.iw1', '432.jk1', '432.ll1'], 'contains': ['1728.q1', '2592.ex1', '2592.fa1', '2592.fd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [325, 31658054504, 37885034880, 41091127], 'label': '46656.ir.864.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '864.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713666
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.db1', '288.di1', '288.dk1', '432.eh1', '432.gg1', '432.lm1'], 'contains': ['1728.r1', '2592.ey1', '2592.fb1', '2592.fd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [301891126320, 325, 104, 41091127], 'label': '46656.ir.864.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '864.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713667
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.di1', '288.dj1', '288.dk1', '432.x1', '432.ei1', '432.gh1', '432.hl1', '432.jl1', '432.kz1', '432.ln1'], 'contains': ['1728.s1', '2592.ez1', '2592.fc1', '2592.fd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 325, 104, 41091127], 'label': '46656.ir.864.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '864.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713668
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.dg1', '432.ce1', '432.hm1', '432.ly1'], 'contains': ['1728.u1', '2592.fe1', '2592.ff1', '2592.fg1', '2592.fj1', '2592.fk1', '2592.fm1', '2592.fn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1481684835, 269279866800, 37885034880, 41091127], 'label': '46656.ir.864.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '864.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fx1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713669
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.df1', '432.cf1'], 'contains': ['1728.v1', '2592.ff1', '2592.fg1', '2592.fo1', '2592.fp1', '2592.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [270715783064, 37885034880, 41091127, 269279867125], 'label': '46656.ir.864.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.cf1', 'old_label': '864.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fy1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713670
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fy2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.df1', '432.cf2'], 'contains': ['1728.v2', '2592.ff1', '2592.fg1', '2592.fo2', '2592.fp2', '2592.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [355419187304, 37885034880, 41091127, 269279867125], 'label': '46656.ir.864.fy2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '864.fy2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fy2', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713671
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.df1', '288.dg1', '432.cg1', '432.hn1', '432.kb1'], 'contains': ['1728.w1', '2592.ff1', '2592.fg1', '2592.fh1', '2592.fl1', '2592.fn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1481684835, 268280812800, 37885034880, 41091127], 'label': '46656.ir.864.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '864.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.fz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216713672
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '18.a1'], 'contains': ['72.d1', '72.h1', '72.i1', '72.do1', '72.dp1', '72.fj1', '72.fk1', '108.d1', '108.f1', '324.b1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 1174819, 1481684400, 39916800, 6227827207, 7, 325], 'label': '46656.ir.36.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713673
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dc1', '288.dg1', '432.ch1', '432.cr1', '432.ho1', '432.kc1', '432.lz1'], 'contains': ['1728.a1', '2592.fe1', '2592.fh1', '2592.fi1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800, 41091127], 'label': '46656.ir.864.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ga1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216713674
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dd1', '288.dg1', '288.dh1', '432.hp1'], 'contains': ['1728.x1', '2592.fi1', '2592.fj1', '2592.fl1', '2592.fm1', '2592.fn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [39366316080, 1481684504, 269279866800, 41091127], 'label': '46656.ir.864.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ew1', 'old_label': '864.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gb1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216713675
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.dh1'], 'contains': ['1728.bc1', '2592.fj1', '2592.fk1', '2592.fo1', '2592.fo2', '2592.fp1', '2592.fp2', '2592.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [356381953304, 301891126320, 355419187525, 41091127], 'label': '46656.ir.864.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.gc1', 'old_label': '864.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gc1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 216713676
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.de1', '288.df1', '288.dh1', '432.hq1'], 'contains': ['1728.bh1', '2592.fl1', '2592.fm1', '2592.fn1', '2592.fo1', '2592.fo2', '2592.fp2', '2592.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [356381953304, 39366316080, 355419187525, 41091127], 'label': '46656.ir.864.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq1', 'old_label': '864.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gd1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713677
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.de1', '288.df1', '288.dh1', '432.hq2'], 'contains': ['1728.bh2', '2592.fl1', '2592.fm1', '2592.fn1', '2592.fo1', '2592.fo2', '2592.fp1', '2592.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [356381953304, 39366316080, 41091127, 269279867125], 'label': '46656.ir.864.gd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq2', 'old_label': '864.gd2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gd2', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713678
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dl1', '288.dn1', '288.dt1', '432.bt1', '432.du1', '432.ft1', '432.hf1', '432.in1', '432.jt1', '432.md1'], 'contains': ['1728.b1', '2592.fr1', '2592.fs1', '2592.fv1', '2592.fy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 435], 'label': '46656.ir.864.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '864.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ge1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713679
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dm1', '288.dn1', '288.du1', '432.p1', '432.dv1', '432.gq1', '432.hg1', '432.io1', '432.kk1', '432.ls1'], 'contains': ['1728.e1', '2592.fr1', '2592.ft1', '2592.fw1', '2592.ga1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684400, 1481684504], 'label': '46656.ir.864.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '864.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gf1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713680
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dn1', '288.do1', '288.dp1', '288.dq1', '288.dr1', '288.ds1', '288.dv1', '432.dw1', '432.hh1', '432.ip1'], 'contains': ['1728.f1', '2592.fr1', '2592.fu1', '2592.fx1', '2592.fz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 39366316080, 269279866800, 435], 'label': '46656.ir.864.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '864.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713681
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dm1', '288.do1', '288.dt1', '432.fu1', '432.hi1', '432.ju1'], 'contains': ['1728.m1', '2592.fr1', '2592.fv1', '2592.gb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812904, 355419187525], 'label': '46656.ir.864.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '864.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gh1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713682
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dl1', '288.do1', '288.du1', '432.q1', '432.hj1', '432.lt1'], 'contains': ['1728.n1', '2592.fr1', '2592.fw1', '2592.gd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 1481684725, 39366316080, 104], 'label': '46656.ir.864.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '864.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gi1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713683
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.a1', '18.b1', '18.j1'], 'contains': ['72.d1', '72.e1', '72.j1', '72.k1', '72.m1', '72.dg1', '72.dv1', '72.er1', '72.fv1', '72.gb1', '72.gl1', '108.a1', '108.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6227827207, 7], 'label': '46656.ir.36.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713684
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dl1', '288.dm1', '288.do1', '288.dv1', '432.hk1'], 'contains': ['1728.o1', '2592.fr1', '2592.fx1', '2592.gc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 39366316080, 104, 269279867125], 'label': '46656.ir.864.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hk1', 'old_label': '864.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gj1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713685
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dt1', '288.du1', '288.dv1', '432.r1', '432.em1', '432.fv1', '432.hl1', '432.ii1', '432.jv1', '432.lu1'], 'contains': ['1728.s1', '2592.fr1', '2592.gg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 325, 104], 'label': '46656.ir.864.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '864.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gk1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216713686
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dl1', '288.dn1', '432.bu1', '432.hm1', '432.me1'], 'contains': ['1728.u1', '2592.fs1', '2592.fw1', '2592.fx1', '2592.gi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684835, 268280812800], 'label': '46656.ir.864.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '864.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713687
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dm1', '288.dn1', '432.gr1', '432.hn1', '432.kl1'], 'contains': ['1728.w1', '2592.ft1', '2592.fv1', '2592.fx1', '2592.go1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 39366316080, 270715783064, 1481684400], 'label': '46656.ir.864.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iu1', 'old_label': '864.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713688
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dn1', '288.dw1', '288.dx1', '432.bv1', '432.ct1', '432.gs1', '432.ho1', '432.it1', '432.km1', '432.mf1'], 'contains': ['1728.a1', '2592.fs1', '2592.ft1', '2592.fu1', '2592.gh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684400, 269279866800], 'label': '46656.ir.864.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '864.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216713689
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dn1', '288.do1', '288.dy1', '288.dz1', '288.ea1', '288.ea2', '432.hp1'], 'contains': ['1728.x1', '2592.fu1', '2592.fv1', '2592.fw1', '2592.fx1', '2592.gj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684504, 269279866800], 'label': '46656.ir.864.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hp1', 'old_label': '864.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.go1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713690
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dp1', '288.dw1', '288.dy1', '432.cu1', '432.hy1', '432.iq1'], 'contains': ['1728.y1', '2592.fu1', '2592.gk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 655477406640, 269279866800], 'label': '46656.ir.864.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '864.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gp1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713691
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dp1', '288.dq1', '288.dx1', '288.dz1', '288.ea1', '288.ea2', '432.ir1'], 'contains': ['1728.z1', '2592.fu1', '2592.gl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 39366316080, 188938194828, 269279866800], 'label': '46656.ir.864.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ir1', 'old_label': '864.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gq1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713692
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dr1', '288.dw1', '288.dz1', '432.cv1'], 'contains': ['1728.ba1', '2592.fu1', '2592.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 39366316080, 269279866800, 623823424560], 'label': '46656.ir.864.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '864.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gr1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216713693
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dr1', '288.ds1', '288.dx1', '288.dy1', '288.dz1', '288.ea1', '288.ea2'], 'contains': ['1728.bb1', '2592.fu1', '2592.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [6267744007, 39366316080, 456583967628, 269279866800], 'label': '46656.ir.864.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.gs1', 'old_label': '864.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gs1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216713694
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.a1', '18.c1', '18.k1'], 'contains': ['72.e1', '72.f1', '72.i1', '72.ec1', '72.ed1', '72.es1', '72.eu1', '108.h1', '108.j1', '324.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39957120, 1134000, 268280812800, 37885034880, 499, 7, 325, 31697930984], 'label': '46656.ir.36.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713695
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dl1', '288.dm1', '288.do1', '432.hq1'], 'contains': ['1728.bh1', '2592.fv1', '2592.fw1', '2592.fx1', '2592.gp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 356381953304, 39366316080, 355419187525], 'label': '46656.ir.864.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq1', 'old_label': '864.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gt1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713696
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gt2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['288.dl1', '288.dm1', '288.do1', '432.hq2'], 'contains': ['1728.bh2', '2592.fv1', '2592.fw1', '2592.fx1', '2592.gp2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [6267744007, 356381953304, 39366316080, 269279867125], 'label': '46656.ir.864.gt2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq2', 'old_label': '864.gt2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gt2', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216713697
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dn1', '288.eb1', '432.bw1', '432.dx1', '432.gb1', '432.gt1', '432.im1', '432.jt1', '432.lp1'], 'contains': ['1728.b1', '2592.fy1', '2592.fz1', '2592.ga1', '2592.gh1', '2592.gi1', '2592.gj1', '2592.go1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 40323593520], 'label': '46656.ir.864.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '864.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gu1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216713698
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dl1', '288.eb1', '432.bx1', '432.gc1', '432.lq1'], 'contains': ['1728.c1', '2592.fy1', '2592.gc1', '2592.gd1', '2592.gi1', '2592.gp1', '2592.gp2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 268280812800, 301891126645, 355419187304], 'label': '46656.ir.864.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '864.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gv1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713699
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.do1', '288.eb1', '432.gd1'], 'contains': ['1728.g1', '2592.fz1', '2592.gb1', '2592.gc1', '2592.gd1', '2592.gj1', '2592.gp1', '2592.gp2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 268280813125, 301891126320, 355419187304], 'label': '46656.ir.864.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ek1', 'old_label': '864.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gw1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 216713700
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dp1', '288.ec1', '432.dy1', '432.hc1', '432.id1'], 'contains': ['1728.i1', '2592.fz1', '2592.ge1', '2592.gk1', '2592.gl1', '2592.gq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 555805963521, 294706903784, 388956924720], 'label': '46656.ir.864.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '864.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gx1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216713701
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dq1', '288.ec1', '432.ie1'], 'contains': ['1728.j1', '2592.fz1', '2592.gf1', '2592.gl1', '2592.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 301891126320, 325, 462811064028], 'label': '46656.ir.864.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fd1', 'old_label': '864.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gy1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216713702
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dr1', '288.ed1', '432.dz1'], 'contains': ['1728.k1', '2592.fz1', '2592.gm1', '2592.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 294706903784, 388956924720, 112217454801], 'label': '46656.ir.864.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bw1', 'old_label': '864.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.gz1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 216713703
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ds1', '288.ed1'], 'contains': ['1728.l1', '2592.fz1', '2592.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [6267744007, 461333739315, 301891126320, 104], 'label': '46656.ir.864.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ds1', 'old_label': '864.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ha1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 216713704
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.dm1', '288.eb1', '432.ge1', '432.gu1', '432.ju1'], 'contains': ['1728.m1', '2592.ga1', '2592.gb1', '2592.gc1', '2592.go1', '2592.gp1', '2592.gp2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 301891126645, 40323593520, 355419187304], 'label': '46656.ir.864.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fz1', 'old_label': '864.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hb1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713705
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '18.c1', '18.d1', '18.j1'], 'contains': ['72.e1', '72.n1', '72.o1', '72.et1', '72.ew1', '72.gu1', '72.gv1', '108.b1', '324.n1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400, 1481684504, 39916800, 1174645], 'label': '46656.ir.36.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713706
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ec1', '432.hd1'], 'contains': ['1728.p1', '2592.gc1', '2592.ge1', '2592.gf1', '2592.gq1', '2592.gr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 294706903784, 325, 174451657230], 'label': '46656.ir.864.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hd1', 'old_label': '864.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hc1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 216713707
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dt1', '288.eb1', '432.by1', '432.en1', '432.fw1', '432.gf1', '432.if1', '432.iz1', '432.lr1'], 'contains': ['1728.q1', '2592.fy1', '2592.gb1', '2592.gg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 268280812800, 325, 355419187304], 'label': '46656.ir.864.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '864.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hd1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713708
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dv1', '288.eb1', '288.ec1', '288.ed1', '432.eo1', '432.gg1', '432.ig1'], 'contains': ['1728.r1', '2592.fz1', '2592.gc1', '2592.gg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 301891126320, 325, 104], 'label': '46656.ir.864.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '864.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.he1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713709
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.du1', '288.eb1', '432.s1', '432.ep1', '432.gh1', '432.gv1', '432.ih1', '432.jv1', '432.la1'], 'contains': ['1728.s1', '2592.ga1', '2592.gd1', '2592.gg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744007, 325, 40323593520], 'label': '46656.ir.864.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '864.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hf1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713710
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '864.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jt1', '288.ec1', '432.eq1', '432.he1', '432.hz1'], 'contains': ['1728.t1', '2592.ge1', '2592.gf1', '2592.gg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 325, 174451657230, 104], 'label': '46656.ir.864.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '864.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.hg1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216713711
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1', '324.a1', '324.bi1', '486.a1'], 'contains': ['1944.a1', '1944.i1', '1944.j1', '1944.cr1', '1944.cs1', '1944.en1', '1944.eo1', '2916.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [499, 443130957804, 270715782960, 40320, 270715783404], 'label': '46656.ir.972.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216713712
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1', '324.b1', '324.bj1', '486.a1'], 'contains': ['1944.a1', '1944.k1', '1944.l1', '1944.ct1', '1944.cu1', '1944.ep1', '1944.eq1', '2916.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 41051299, 270715782960, 40320, 270715783404], 'label': '46656.ir.972.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713713
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1', '324.a1', '324.bk1', '486.a1'], 'contains': ['1944.b1', '1944.i1', '1944.k1', '1944.cy1', '1944.cz1', '1944.ex1', '1944.ey1', '2916.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [499, 443130957804, 444, 269279866800, 40320], 'label': '46656.ir.972.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '972.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713714
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1', '324.b1', '324.bl1', '486.a1'], 'contains': ['1944.b1', '1944.j1', '1944.l1', '1944.da1', '1944.db1', '1944.ez1', '1944.fa1', '2916.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41051299, 443130957804, 444, 269279866800, 40320], 'label': '46656.ir.972.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713715
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.c1', '324.i1', '324.bm1', '486.a1'], 'contains': ['1944.a1', '1944.b1', '1944.d1', '1944.p1', '1944.s1', '1944.t1', '1944.z1', '1944.ck1', '1944.cx1', '1944.de1', '1944.ec1', '1944.fk1', '1944.fw1', '1944.fx1', '1944.gv1', '2916.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 39916800, 6227827207], 'label': '46656.ir.972.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713716
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '18.b1', '18.d1', '18.k1'], 'contains': ['72.e1', '72.g1', '72.ee1', '72.ev1', '72.ey1', '108.i1', '324.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39957120, 1134000, 268280812800, 37885034880, 7, 41051299, 325, 31697930984], 'label': '46656.ir.36.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713717
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.h1', '324.d1', '324.bp1', '486.o1'], 'contains': ['1944.c1', '1944.e1', '1944.h1', '1944.dh1', '1944.di1', '1944.ed1', '1944.ee1', '2916.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [31697931324, 39957120, 499, 1134000, 37885034880], 'label': '46656.ir.972.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '972.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713718
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.i1', '324.f1', '324.bq1', '486.o1'], 'contains': ['1944.c1', '1944.f1', '1944.g1', '1944.di1', '1944.dj1', '1944.ef1', '1944.eg1', '2916.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [31697931324, 39957120, 41051299, 1134000, 37885034880], 'label': '46656.ir.972.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '972.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713719
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1', '324.d1', '324.bn1', '486.a1'], 'contains': ['1944.d1', '1944.i1', '1944.l1', '1944.dn1', '1944.do1', '1944.eh1', '1944.ei1', '2916.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [387037284480, 39957120, 499, 39957564, 1134000], 'label': '46656.ir.972.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713720
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1', '324.g1', '324.bo1', '486.a1'], 'contains': ['1944.d1', '1944.j1', '1944.k1', '1944.dp1', '1944.dq1', '1944.ej1', '1944.ek1', '2916.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [469, 39366316080, 1174320, 39916800, 6227827818], 'label': '46656.ir.972.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713721
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.i1', '324.l1', '324.br1', '486.m1'], 'contains': ['1944.m1', '1944.n1', '1944.o1', '1944.r1', '1944.v1', '1944.fd1', '1944.fe1', '1944.ff1', '1944.fj1', '1944.fn1', '1944.ga1', '2916.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [7, 1174320, 39916800, 6227827207, 104], 'label': '46656.ir.972.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713722
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.b1', '324.n1', '324.bt1', '486.m1'], 'contains': ['1944.n1', '1944.w1', '1944.x1', '1944.fg1', '1944.fh1', '1944.gi1', '1944.gj1', '2916.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 7, 1174320, 39916800, 104], 'label': '46656.ir.972.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713723
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.l1', '324.r1', '324.bw1', '486.m1'], 'contains': ['1944.r1', '1944.u1', '1944.x1', '1944.fq1', '1944.fr1', '1944.gb1', '1944.gc1', '2916.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 1174320, 39916800, 39957127, 435], 'label': '46656.ir.972.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.l1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713724
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.m1', '324.t1', '324.cb1', '486.m1'], 'contains': ['1944.u1', '1944.v1', '1944.w1', '1944.gn1', '1944.go1', '1944.gq1', '1944.gr1', '2916.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [1174320, 39916800, 6227827207, 39957127, 104], 'label': '46656.ir.972.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.m1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713725
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.by1', '324.v1', '486.b1', '486.c1', '486.n1'], 'contains': ['1944.ba1', '1944.bd1', '1944.bk1', '1944.cv1', '1944.dt1', '1944.fm1', '1944.gg1', '2916.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 40320, 6227827207], 'label': '46656.ir.972.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.n1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713726
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bz1', '324.w1', '486.d1', '486.e1', '486.n1'], 'contains': ['1944.ba1', '1944.bg1', '1944.bn1', '1944.dr1', '1944.dw1', '1944.gd1', '1944.gh1', '2916.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 7, 1174320, 40320], 'label': '46656.ir.972.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.o1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713727
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.a1', '18.d1', '18.l1'], 'contains': ['72.e1', '72.h1', '72.ef1', '72.ex1', '72.ez1', '108.k1', '324.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 7, 6227827818], 'label': '46656.ir.36.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713728
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.p1', '324.cc1', '486.b1', '486.d1', '486.o1'], 'contains': ['1944.e1', '1944.f1', '1944.ba1', '1944.ds1', '1944.du1', '2916.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 499, 1481684400, 1521641964, 39916800], 'label': '46656.ir.972.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713729
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.q1', '324.cd1', '486.c1', '486.e1', '486.o1'], 'contains': ['1944.g1', '1944.h1', '1944.ba1', '1944.dv1', '1944.dy1', '2916.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41051299, 1481684400, 1521641964, 39916800], 'label': '46656.ir.972.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713730
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.r1', '108.cc1', '486.b1', '486.e1', '486.p1'], 'contains': ['1944.ba1', '1944.dx1', '1944.ea1', '2916.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 1174320, 6227827818, 40320], 'label': '46656.ir.972.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.r1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713731
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.s1', '108.cd1', '486.c1', '486.d1', '486.p1'], 'contains': ['1944.ba1', '1944.dz1', '1944.eb1', '2916.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 1174320, 6267381738, 40320], 'label': '46656.ir.972.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713732
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ce1', '324.v1', '324.x1', '486.m1'], 'contains': ['1944.bb1', '1944.bc1', '1944.bl1', '1944.fe1', '1944.fg1', '1944.fq1', '1944.gn1', '2916.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1174320, 6227827207, 7, 104, 40320], 'label': '46656.ir.972.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '972.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713733
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cf1', '324.w1', '324.y1', '486.m1'], 'contains': ['1944.bb1', '1944.bf1', '1944.bm1', '1944.ff1', '1944.fh1', '1944.gb1', '1944.go1', '2916.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 7, 1174320, 40320, 104], 'label': '46656.ir.972.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.u1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713734
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cg1', '324.bd1', '324.be1', '324.bf1', '486.m1'], 'contains': ['1944.bc1', '1944.bh1', '1944.bm1', '1944.fn1', '1944.fr1', '1944.gi1', '1944.gr1', '2916.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 1174320, 40320, 39957127, 104], 'label': '46656.ir.972.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713735
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ci1', '324.bd1', '486.n1'], 'contains': ['1944.bd1', '1944.bi1', '1944.bn1', '1944.fo1', '1944.fs1', '1944.gk1', '1944.gs1', '2916.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 40320, 39957127], 'label': '46656.ir.972.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.w1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713736
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.ch1', '324.bd1', '324.be1'], 'contains': ['1944.be1', '1944.bj1', '1944.bo1', '1944.fp1', '1944.ft1', '1944.gm1', '1944.gt1', '2916.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [355419187635, 6267381127, 1174320, 40320, 39957127], 'label': '46656.ir.972.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '972.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.x1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713737
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cj1', '324.bg1', '324.bh1', '486.m1'], 'contains': ['1944.bf1', '1944.bh1', '1944.bl1', '1944.ga1', '1944.gc1', '1944.gj1', '1944.gq1', '2916.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [1174320, 6227827207, 39957127, 104, 40320], 'label': '46656.ir.972.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.y1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713835
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l1', '432.m1', '432.bo1', '648.dh1'], 'contains': ['2592.g1', '2592.dj1', '2592.ei1', '3888.k1', '3888.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [270715783064, 1481684400, 40320, 39957127], 'label': '46656.ir.1296.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '1296.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713738
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '18.b1', '18.c1', '18.l1'], 'contains': ['72.e1', '72.p1', '72.fa1', '72.fb1', '72.gj1', '324.h1', '324.q1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 7, 6267381738], 'label': '46656.ir.36.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713739
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ck1', '324.bh1', '486.n1'], 'contains': ['1944.bg1', '1944.bi1', '1944.bk1', '1944.ge1', '1944.gf1', '1944.gl1', '1944.gp1', '2916.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 40320, 6227827207, 39957127], 'label': '46656.ir.972.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.z1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713740
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.be1', '324.bi1', '324.bk1', '486.f1'], 'contains': ['1944.bp1', '1944.br1', '1944.bt1', '1944.cl1', '1944.cm1', '1944.er1', '1944.es1', '2916.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 499, 443130957804, 40320, 37885034880], 'label': '46656.ir.972.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '972.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713741
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bf1', '324.bj1', '324.bl1', '486.f1'], 'contains': ['1944.bp1', '1944.bt1', '1944.bu1', '1944.cn1', '1944.co1', '1944.et1', '1944.eu1', '2916.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 31658054844, 41051299, 40320, 37885034880], 'label': '46656.ir.972.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '972.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713742
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bm1', '324.br1', '486.f1', '486.g1', '486.n1'], 'contains': ['1944.bp1', '1944.bq1', '1944.bv1', '1944.bw1', '1944.cb1', '1944.ci1', '1944.cv1', '1944.dr1', '1944.fl1', '1944.fo1', '1944.ge1', '2916.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 39916800, 6227827207], 'label': '46656.ir.972.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713743
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bq1', '324.bs1', '486.h1', '486.i1', '486.j1'], 'contains': ['1944.by1', '1944.el1', '1944.gx1', '2916.s1', '3888.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [7, 655477406640, 39916800, 2957880240, 31697930880], 'label': '46656.ir.972.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713744
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bi1', '324.bn1', '324.bp1', '486.f1', '486.k1', '486.o1'], 'contains': ['1944.bq1', '1944.br1', '1944.bu1', '1944.dh1', '1944.dj1', '1944.ds1', '1944.dv1', '2916.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 499, 1481684400, 1521641964, 1134000], 'label': '46656.ir.972.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713745
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1', '324.bt1', '486.k1', '486.l1', '486.n1'], 'contains': ['1944.bq1', '1944.cc1', '1944.cd1', '1944.dt1', '1944.dw1', '1944.gk1', '1944.gl1', '2916.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 7, 1174320, 39916800], 'label': '46656.ir.972.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713746
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bk1', '324.bq1', '486.g1', '486.l1', '486.o1'], 'contains': ['1944.bq1', '1944.bs1', '1944.di1', '1944.du1', '1944.dy1', '2916.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41051299, 1481684400, 1521641964, 1134000], 'label': '46656.ir.972.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713747
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bl1', '324.bo1', '486.f1', '486.l1', '486.p1'], 'contains': ['1944.bq1', '1944.bt1', '1944.dk1', '1944.dx1', '1944.dz1', '2916.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 1174320, 39916800, 6227827818], 'label': '46656.ir.972.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713748
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bc1', '108.bm1', '486.g1', '486.k1', '486.p1'], 'contains': ['1944.bq1', '1944.ce1', '1944.ea1', '1944.eb1', '1944.fz1', '2916.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 1174320, 39916800, 6267381738], 'label': '46656.ir.972.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713749
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '18.j1'], 'contains': ['72.k1', '72.l1', '72.o1', '72.gd1', '72.gg1', '72.gm1', '72.gn1', '108.l1', '324.r1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 39916800, 39957127, 1174645], 'label': '46656.ir.36.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713750
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bs1', '324.bu1', '324.ce1', '486.m1'], 'contains': ['1944.n1', '1944.u1', '1944.bb1', '1944.bh1', '1944.bx1', '1944.fi1', '1944.gy1', '2916.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39957224, 39916800], 'label': '46656.ir.972.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '972.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713751
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cm1', '324.bv1', '324.bx1', '324.cf1', '486.m1'], 'contains': ['1944.r1', '1944.w1', '1944.bc1', '1944.bf1', '1944.bx1', '1944.fu1', '1944.gu1', '2916.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 41050800, 39957224, 39916800, 6227827200], 'label': '46656.ir.972.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '972.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713752
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bp1', '324.bw1', '486.n1'], 'contains': ['1944.bw1', '1944.ca1', '1944.cd1', '1944.fm1', '1944.fs1', '1944.gd1', '1944.gf1', '2916.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 39916800, 39957127], 'label': '46656.ir.972.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713753
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '324.bx1', '486.h1'], 'contains': ['1944.by1', '1944.fy1', '1944.gw1', '2916.t1', '3888.dw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [655477406640, 39916800, 6227827200, 2957880240, 31697930880], 'label': '46656.ir.972.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '972.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713754
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.cn1', '324.by1', '324.bz1', '324.ca1', '324.cg1', '486.m1'], 'contains': ['1944.v1', '1944.x1', '1944.bl1', '1944.bm1', '1944.bx1', '1944.gz1', '1944.hc1', '2916.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39957120, 41050800, 39957224, 39916800, 6227827207], 'label': '46656.ir.972.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713755
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bu1', '324.by1', '486.h1'], 'contains': ['1944.by1', '1944.ha1', '1944.hd1', '2916.u1', '3888.ef1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [655477406640, 39916800, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.972.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bo1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713756
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bv1', '324.by1', '324.bz1'], 'contains': ['1944.bz1', '1944.hb1', '1944.he1', '2916.u1', '3888.eg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [722937882588, 37924992000, 39916800, 1520467200, 6227827207], 'label': '46656.ir.972.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.bp1', 'old_label': '972.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bp1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713757
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bs1', '324.cb1', '486.n1'], 'contains': ['1944.ca1', '1944.cb1', '1944.cc1', '1944.gg1', '1944.gh1', '1944.gp1', '1944.gs1', '2916.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 6227827207, 39957127], 'label': '46656.ir.972.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713758
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bt1', '324.cc1', '324.cj1', '486.o1'], 'contains': ['1944.e1', '1944.g1', '1944.br1', '1944.bs1', '1944.cf1', '1944.ed1', '1944.ef1', '2916.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31697931324, 39957120, 499, 39916800, 37885034880], 'label': '46656.ir.972.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '972.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713759
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bu1', '324.cd1', '324.ck1', '486.o1'], 'contains': ['1944.f1', '1944.h1', '1944.bs1', '1944.bu1', '1944.cf1', '1944.ee1', '1944.eg1', '2916.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [31697931324, 39957120, 41051299, 39916800, 37885034880], 'label': '46656.ir.972.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '972.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713760
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '18.j1'], 'contains': ['72.l1', '72.m1', '72.n1', '72.gy1', '72.gz1', '72.hb1', '72.he1', '108.m1', '324.t1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6227827207, 39957127], 'label': '46656.ir.36.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713761
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ce1', '324.cp1', '486.n1', '486.o1', '486.p1'], 'contains': ['1944.c1', '1944.y1', '1944.ba1', '1944.bi1', '1944.bq1', '1944.ca1', '1944.cf1', '1944.cg1', '1944.ch1', '1944.em1', '1944.hg1', '2916.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39916800, 37885034880], 'label': '46656.ir.972.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713762
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cp1', '324.cf1', '486.n1'], 'contains': ['1944.bd1', '1944.bg1', '1944.bw1', '1944.cc1', '1944.ch1', '1944.fv1', '1944.hf1', '2916.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 39916800, 6227827200], 'label': '46656.ir.972.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '972.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713763
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cq1', '324.cg1', '486.n1'], 'contains': ['1944.bk1', '1944.bn1', '1944.cb1', '1944.cd1', '1944.ch1', '1944.hh1', '1944.hi1', '2916.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 39916800, 6227827207], 'label': '46656.ir.972.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713764
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ds1', '324.cs1', '324.cv1', '486.f1'], 'contains': ['1944.ci1', '1944.cl1', '1944.co1', '1944.dh1', '1944.dk1', '1944.er1', '1944.et1', '2916.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 31658054844, 41091120, 499, 37885034880], 'label': '46656.ir.972.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '972.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713765
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dt1', '324.ct1', '324.cw1', '486.f1'], 'contains': ['1944.ci1', '1944.cm1', '1944.cn1', '1944.dj1', '1944.dk1', '1944.es1', '1944.eu1', '2916.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 31658054844, 41091120, 41051299, 37885034880], 'label': '46656.ir.972.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '972.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713766
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.du1', '324.cs1', '324.cu1', '324.cz1'], 'contains': ['1944.cj1', '1944.cp1', '1944.cq1', '1944.dl1', '1944.dm1', '1944.ev1', '1944.ew1', '2916.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [180790853484, 41091120, 301891126320, 499, 444], 'label': '46656.ir.972.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '972.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.by1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713767
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dv1', '324.cs1', '324.cx1', '486.a1'], 'contains': ['1944.ck1', '1944.cr1', '1944.cu1', '1944.dn1', '1944.dp1', '1944.ex1', '1944.ez1', '2916.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 41091120, 499, 270715782960, 270715783404], 'label': '46656.ir.972.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.bz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713768
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dw1', '324.ct1', '324.cy1', '486.a1'], 'contains': ['1944.ck1', '1944.cs1', '1944.ct1', '1944.do1', '1944.dq1', '1944.ey1', '1944.fa1', '2916.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 41091120, 41051299, 270715782960, 270715783404], 'label': '46656.ir.972.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ca1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713769
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dx1', '324.da1', '486.b1', '486.f1', '486.q1'], 'contains': ['1944.cl1', '1944.cn1', '1944.cv1', '1944.ds1', '1944.dx1', '2916.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 499, 443130957804, 37885034880], 'label': '46656.ir.972.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713770
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cv1', '108.dy1', '486.b1', '486.g1', '486.r1'], 'contains': ['1944.cv1', '1944.du1', '1944.ea1', '2916.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 39917299, 443130957804, 37885034880], 'label': '46656.ir.972.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713771
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.g1', '12.h1', '12.k1', '12.bp1', '12.bq1', '12.br1', '12.bu1', '18.c1', '54.h1', '54.o1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6267381127, 499, 7, 269279866800], 'label': '46656.ir.6.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713772
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '18.p1'], 'contains': ['72.q1', '72.r1', '72.bg1', '72.bj1', '72.bn1', '72.cs1', '72.ct1', '72.cv1', '72.fx1', '72.ga1', '72.go1', '108.a1', '108.x1', '108.bd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 39916800, 6227827207, 7, 269279866800], 'label': '46656.ir.36.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216713773
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dz1', '324.db1', '486.c1', '486.f1', '486.r1'], 'contains': ['1944.cm1', '1944.co1', '1944.cv1', '1944.dv1', '1944.dz1', '2916.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 40819, 443130957804, 37885034880], 'label': '46656.ir.972.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713774
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cw1', '108.ea1', '486.c1', '486.g1', '486.q1'], 'contains': ['1944.cv1', '1944.dy1', '1944.eb1', '2916.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 443130957804, 39957619, 37885034880], 'label': '46656.ir.972.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ce1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713775
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cx1', '324.ea1', '486.n1', '486.q1', '486.r1'], 'contains': ['1944.cv1', '1944.dw1', '1944.em1', '1944.fs1', '1944.fv1', '1944.gp1', '1944.hh1', '2916.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 7, 6227827207], 'label': '46656.ir.972.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713776
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ec1', '243.a1', '324.cu1'], 'contains': ['1944.cw1', '1944.dc1', '1944.dd1', '1944.df1', '1944.dg1', '1944.fb1', '1944.fc1', '2916.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 499, 93576273840, 444, 6227389164], 'label': '46656.ir.972.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '972.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713777
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ed1', '324.cv1', '324.cx1', '324.cz1', '486.a1'], 'contains': ['1944.cx1', '1944.cy1', '1944.db1', '1944.dn1', '1944.dq1', '1944.en1', '1944.ep1', '2916.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 499, 443130957804, 444, 269279866800], 'label': '46656.ir.972.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ch1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713778
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ee1', '324.cw1', '324.cy1', '486.a1'], 'contains': ['1944.cx1', '1944.cz1', '1944.da1', '1944.do1', '1944.dp1', '1944.eo1', '1944.eq1', '2916.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 41051299, 443130957804, 444, 269279866800], 'label': '46656.ir.972.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713779
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ef1', '324.da1', '324.dc1', '486.a1'], 'contains': ['1944.cr1', '1944.ct1', '1944.cy1', '1944.da1', '1944.de1', '1944.eh1', '1944.ej1', '2916.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41050800, 499, 443130957804, 444, 269279866800], 'label': '46656.ir.972.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '972.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713780
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.eg1', '324.db1', '324.dd1', '486.a1'], 'contains': ['1944.cs1', '1944.cu1', '1944.cz1', '1944.db1', '1944.de1', '1944.ei1', '1944.ek1', '2916.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [40819, 41050800, 443130957804, 444, 269279866800], 'label': '46656.ir.972.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ck1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713781
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bx1', '324.eb1', '486.h1', '486.s1', '486.t1'], 'contains': ['1944.el1', '1944.fy1', '1944.ha1', '2916.bb1', '3888.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [7, 655477406640, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.972.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cl1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713782
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ei1', '324.dh1', '486.d1', '486.f1', '486.w1'], 'contains': ['1944.dr1', '1944.ds1', '1944.dz1', '1944.er1', '1944.eu1', '2916.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 355419187337, 268280812800, 7, 1174320], 'label': '46656.ir.972.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713783
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '18.p1'], 'contains': ['72.r1', '72.bo1', '72.bp1', '72.cw1', '72.cx1', '72.gs1', '72.gt1', '108.b1', '108.z1', '324.bt1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 39916800, 6267381127, 7, 269279866800], 'label': '46656.ir.36.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216713784
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.db1', '108.ej1', '486.d1', '486.g1', '486.x1'], 'contains': ['1944.dr1', '1944.du1', '1944.eb1', '2916.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320, 274468360462], 'label': '46656.ir.972.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713785
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ek1', '324.di1', '486.e1', '486.f1', '486.x1'], 'contains': ['1944.dr1', '1944.dv1', '1944.dx1', '1944.es1', '1944.et1', '2916.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320, 274508640142], 'label': '46656.ir.972.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.co1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713786
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dc1', '108.el1', '486.e1', '486.g1', '486.w1'], 'contains': ['1944.dr1', '1944.dy1', '1944.ea1', '2916.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320, 355459144457], 'label': '46656.ir.972.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713787
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dd1', '108.em1', '486.b1', '486.k1', '486.w1'], 'contains': ['1944.ds1', '1944.dt1', '1944.ea1', '2916.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [355419187337, 268280812800, 7, 1174320, 6227464327], 'label': '46656.ir.972.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713788
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.de1', '108.en1', '486.d1', '486.k1', '486.q1'], 'contains': ['1944.ds1', '1944.dw1', '1944.eb1', '2916.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 499, 443609999724, 37885034880], 'label': '46656.ir.972.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713789
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dg1', '108.eo1', '486.b1', '486.l1', '486.x1'], 'contains': ['1944.dt1', '1944.du1', '1944.dx1', '2916.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 274508640142], 'label': '46656.ir.972.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cs1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713790
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.df1', '108.ep1', '486.c1', '486.k1', '486.x1'], 'contains': ['1944.dt1', '1944.dv1', '1944.eb1', '2916.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 274468360462], 'label': '46656.ir.972.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.ct1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713791
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dh1', '108.eq1', '486.c1', '486.l1', '486.w1'], 'contains': ['1944.dt1', '1944.dy1', '1944.dz1', '2916.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 355459144457], 'label': '46656.ir.972.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713792
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dj1', '108.er1', '486.d1', '486.l1', '486.r1'], 'contains': ['1944.du1', '1944.dw1', '1944.dz1', '2916.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 39917299, 443609999724, 37885034880], 'label': '46656.ir.972.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713793
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.di1', '108.es1', '486.e1', '486.k1', '486.r1'], 'contains': ['1944.dv1', '1944.dw1', '1944.ea1', '2916.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 40819, 443609999724, 37885034880], 'label': '46656.ir.972.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713794
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '18.e1'], 'contains': ['72.s1', '72.w1', '72.x1', '72.da1', '72.db1', '72.fd1', '72.fe1', '108.c1', '108.be1', '324.bi1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39916800, 268280812800, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.36.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216713795
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dk1', '108.et1', '486.e1', '486.l1', '486.q1'], 'contains': ['1944.dw1', '1944.dx1', '1944.dy1', '2916.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 34136928000, 443609999724, 39957619, 37885034880], 'label': '46656.ir.972.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713796
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.eu1', '324.dh1', '324.dj1', '486.a1'], 'contains': ['1944.ec1', '1944.eh1', '1944.ek1', '1944.en1', '1944.eq1', '1944.ex1', '1944.fa1', '2916.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 137, 7, 1174320], 'label': '46656.ir.972.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713797
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ev1', '324.di1', '324.dk1', '486.a1'], 'contains': ['1944.ec1', '1944.ei1', '1944.ej1', '1944.eo1', '1944.ep1', '1944.ey1', '1944.ez1', '2916.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 6227827342, 7, 1174320], 'label': '46656.ir.972.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '972.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.cz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713798
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.by1', '324.ec1', '486.h1', '486.u1', '486.v1'], 'contains': ['1944.el1', '1944.gw1', '1944.hd1', '2916.bo1', '3888.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 7, 655477406640, 2957880240, 31697930880], 'label': '46656.ir.972.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.da1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713799
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bz1', '108.ex1', '486.i1', '486.s1', '486.u1'], 'contains': ['1944.el1', '2916.bp1', '3888.cs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 499, 39957564, 113215011840, 2957880240], 'label': '46656.ir.972.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.db1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713800
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ca1', '108.ey1', '486.i1', '486.t1', '486.v1'], 'contains': ['1944.el1', '2916.bq1', '3888.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39917299, 39957120, 39957564, 113215011840, 2957880240], 'label': '46656.ir.972.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dc1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713801
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cb1', '108.ez1', '486.j1', '486.s1', '486.v1'], 'contains': ['1944.el1', '2916.br1', '3888.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 655477406640, 6227827818, 2957880240, 31697930880], 'label': '46656.ir.972.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713802
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cc1', '108.fa1', '486.j1', '486.t1', '486.u1'], 'contains': ['1944.el1', '2916.bs1', '3888.cv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 6267744618, 655477406640, 2957880240, 31697930880], 'label': '46656.ir.972.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.de1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713803
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dl1', '324.ed1', '486.n1', '486.w1', '486.x1'], 'contains': ['1944.dr1', '1944.dt1', '1944.em1', '1944.gf1', '1944.gs1', '1944.hf1', '1944.hi1', '2916.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 39957120, 41050800, 7], 'label': '46656.ir.972.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.df1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713804
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fc1', '324.dw1', '486.o1', '486.q1', '486.w1'], 'contains': ['1944.ds1', '1944.dy1', '1944.ed1', '1944.eg1', '1944.em1', '2916.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31697931324, 39957120, 41050800, 499, 37885034880], 'label': '46656.ir.972.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713805
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '18.e1'], 'contains': ['72.s1', '72.y1', '72.z1', '72.dc1', '72.dd1', '72.ff1', '72.fg1', '108.d1', '108.bf1', '324.bj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174819, 39916800, 268280812800, 6227827207, 7, 104, 325], 'label': '46656.ir.36.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713806
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fd1', '324.dx1', '486.o1', '486.r1', '486.x1'], 'contains': ['1944.du1', '1944.dv1', '1944.ee1', '1944.ef1', '1944.em1', '2916.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39917299, 31697931324, 39957120, 41050800, 37885034880], 'label': '46656.ir.972.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713807
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.do1', '108.fe1', '486.p1', '486.q1', '486.x1'], 'contains': ['1944.dx1', '1944.eb1', '1944.em1', '2916.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 39957120, 41050800, 6227827818], 'label': '46656.ir.972.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713808
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.dp1', '108.ff1', '486.p1', '486.r1', '486.w1'], 'contains': ['1944.dz1', '1944.ea1', '1944.em1', '2916.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 39957120, 41050800, 6267744618], 'label': '46656.ir.972.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713809
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dq1', '324.ea1', '324.eb1', '324.ek1', '486.m1'], 'contains': ['1944.fe1', '1944.fh1', '1944.fi1', '1944.fr1', '1944.fu1', '1944.gq1', '1944.gz1', '2916.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39957224, 6227827207], 'label': '46656.ir.972.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713810
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.dr1', '324.ec1', '324.ed1', '324.ex1', '486.m1'], 'contains': ['1944.ff1', '1944.fg1', '1944.fi1', '1944.gc1', '1944.gr1', '1944.gu1', '1944.hc1', '2916.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 7, 39957224], 'label': '46656.ir.972.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713811
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fi1', '324.fc1', '324.fd1', '324.fe1', '486.m1'], 'contains': ['1944.fn1', '1944.fq1', '1944.fu1', '1944.gj1', '1944.go1', '1944.gy1', '1944.hc1', '2916.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39916807, 39957555, 39957120, 41050800, 6227827200], 'label': '46656.ir.972.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713812
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fj1', '324.fd1', '486.n1'], 'contains': ['1944.fm1', '1944.fo1', '1944.fv1', '1944.gh1', '1944.gl1', '1944.hg1', '1944.hi1', '2916.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 6227827200], 'label': '46656.ir.972.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713813
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dp1', '324.fe1', '486.h1'], 'contains': ['1944.fy1', '1944.gx1', '1944.hd1', '2916.bt1', '3888.ea1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 655477406640, 6227827200, 2957880240, 31697930880], 'label': '46656.ir.972.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.do1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713814
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.fm1', '324.fg1', '324.fh1', '324.fi1', '486.m1'], 'contains': ['1944.ga1', '1944.gb1', '1944.gi1', '1944.gn1', '1944.gu1', '1944.gy1', '1944.gz1', '2916.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 39957224, 6227827207], 'label': '46656.ir.972.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '972.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713815
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ds1', '324.fh1', '486.h1'], 'contains': ['1944.gw1', '1944.gx1', '1944.ha1', '2916.bu1', '3888.gl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 655477406640, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.972.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '972.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216713816
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '18.e1'], 'contains': ['72.t1', '72.w1', '72.y1', '72.di1', '72.dj1', '72.fn1', '72.fo1', '108.e1', '108.be1', '324.bk1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 40323593520, 39916800, 268280812800, 6227827207, 499, 7, 325], 'label': '46656.ir.36.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713817
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '972.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.fn1', '324.fi1', '486.n1'], 'contains': ['1944.gd1', '1944.ge1', '1944.gg1', '1944.gk1', '1944.hf1', '1944.hg1', '1944.hh1', '2916.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 6227827207], 'label': '46656.ir.972.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '972.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.dr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216713818
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': ['36.a1', '36.bu1', '36.bv1', '36.ds1', '36.dp1'], 'conjugacy_class_count': 1, 'contained_in': ['432.er1', '432.ez1', '432.fd1', '432.fl1', '648.m1', '648.ha1', '648.hf1', '648.hj1', '648.hu1'], 'contains': ['2592.a1', '11664.l1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [499, 7, 325, 104], 'label': '46656.ir.1296.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1296.a1', 'normal_contained_in': ['48.b1'], 'normal_contains': ['2592.a1'], 'normalizer': '1.a1', 'old_label': '1296.a1', 'projective_image': '46656.ir', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1296.3490', 'quotient_action_kernel_order': 1296, 'quotient_fusion': None, 'short_label': '1296.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713819
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1', '432.z1', '648.a1', '648.b1', '648.c1', '648.d1', '648.e1', '648.f1', '648.de1'], 'contains': ['2592.h1', '2592.q1', '2592.df1', '3888.a1', '3888.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 39916800], 'label': '46656.ir.1296.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216713820
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.b1', '432.c1', '432.bb1', '648.i1', '648.bm1', '648.df1'], 'contains': ['2592.b1', '2592.u1', '2592.dg1', '3888.a1', '3888.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [7, 39916800, 31658054504, 37885034880], 'label': '46656.ir.1296.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '1296.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713821
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.b1', '432.d1', '432.ba1', '648.g1', '648.h1', '648.j1'], 'contains': ['2592.c1', '2592.w1', '2592.dh1', '3888.b1', '3888.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 7, 39916800, 104], 'label': '46656.ir.1296.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '1296.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713822
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1', '432.d1', '432.bc1', '648.k1', '648.l1', '648.m1', '648.n1', '648.o1', '648.p1', '648.bn1'], 'contains': ['2592.a1', '2592.f1', '2592.do1', '3888.c1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 325, 39916800, 104], 'label': '46656.ir.1296.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1296.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.e1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713823
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.e1', '432.f1', '432.bd1', '648.g1', '648.q1', '648.x1'], 'contains': ['2592.c1', '2592.ba1', '2592.cp1', '3888.d1', '3888.e1', '3888.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 39916800, 6227827200, 104], 'label': '46656.ir.1296.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '1296.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713824
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.e1', '432.g1', '432.be1', '648.r1'], 'contains': ['2592.e1', '2592.bd1', '2592.cq1', '3888.d1', '3888.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [34096648424, 39366316405, 39916800, 6227827200], 'label': '46656.ir.1296.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.p1', 'old_label': '1296.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216713825
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.e1', '432.h1', '432.bf1', '648.k1', '648.s1', '648.t1'], 'contains': ['2592.f1', '2592.be1', '2592.cr1', '3888.d1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [325, 39916800, 6227827200, 104], 'label': '46656.ir.1296.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '1296.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.h1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216713826
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.f1', '432.g1', '432.h1', '432.bg1', '648.h1', '648.u1', '648.x1'], 'contains': ['2592.c1', '2592.bk1', '2592.cu1', '3888.d1', '3888.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 39916800, 40323593520, 6227827200], 'label': '46656.ir.1296.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '1296.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713827
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '18.e1'], 'contains': ['72.t1', '72.x1', '72.z1', '72.dk1', '72.dl1', '72.fp1', '72.fq1', '108.f1', '108.bf1', '324.bl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1174819, 40323593624, 40323593520, 39916800, 268280812800, 6227827207, 7, 325], 'label': '46656.ir.36.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713828
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.f1', '432.bi1', '648.a1', '648.v1', '648.y1'], 'contains': ['2592.h1', '2592.bn1', '2592.cy1', '3888.e1', '3888.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800, 6227827200], 'label': '46656.ir.1296.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '1296.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713829
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.f1', '432.g1', '432.bh1', '648.w1'], 'contains': ['2592.i1', '2592.br1', '2592.db1', '3888.f1', '3888.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684835, 39916800, 40323593520, 6227827200], 'label': '46656.ir.1296.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '1296.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713830
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bv1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.i1', '432.j1', '432.bj1', '648.l1', '648.t1', '648.z1', '648.ba1', '648.bb1', '648.bc1', '648.cx1'], 'contains': ['2592.f1', '2592.bw1', '2592.ch1', '3888.h1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 325, 39957224, 1134000], 'label': '46656.ir.1296.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.l1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216713831
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.i1', '432.k1', '432.bl1', '648.i1', '648.bd1', '648.dj1'], 'contains': ['2592.b1', '2592.bx1', '2592.ci1', '3888.h1', '3888.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39957120, 31697931315, 1134000, 37885034880], 'label': '46656.ir.1296.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bv1', 'old_label': '1296.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713832
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.j1', '432.k1', '432.bk1', '648.j1', '648.x1', '648.be1'], 'contains': ['2592.c1', '2592.bz1', '2592.cj1', '3888.h1', '3888.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39957555, 387037284480, 39957120, 1134000], 'label': '46656.ir.1296.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '1296.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713833
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.k1', '432.bm1', '648.b1', '648.y1', '648.bf1', '648.bg1', '648.bh1', '648.bi1', '648.dq1'], 'contains': ['2592.h1', '2592.cd1', '2592.co1', '3888.i1', '3888.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 1134000, 37885034880], 'label': '46656.ir.1296.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1296.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.o1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713834
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l1', '432.m1', '432.n1', '432.bn1', '648.bd1', '648.bm1', '648.dg1'], 'contains': ['2592.b1', '2592.dg1', '2592.eg1', '3888.k1', '3888.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1481684400, 1481684504, 40320, 39957127], 'label': '46656.ir.1296.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '1296.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714311
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gd1', '486.s1', '648.ek1', '972.cg1'], 'contains': ['3888.bl1', '3888.cs1', '3888.ct1', '5832.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [624302789040, 499, 444, 6227389164], 'label': '46656.ir.1944.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1944.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713836
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.m1', '432.bp1', '648.bf1', '648.de1', '648.di1'], 'contains': ['2592.h1', '2592.dk1', '2592.ek1', '3888.k1', '3888.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800, 39957127], 'label': '46656.ir.1296.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713837
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.m1', '432.o1', '432.br1', '648.bd1', '648.bt1', '648.df1'], 'contains': ['2592.b1', '2592.dm1', '2592.el1', '3888.l1', '3888.m1', '3888.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [355419187635, 268280812800, 40320, 39957127], 'label': '46656.ir.1296.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '1296.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713838
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.e1'], 'contains': ['72.s1', '72.t1', '72.u1', '72.be1', '72.bh1', '72.bi1', '72.bl1', '72.cz1', '72.df1', '72.du1', '72.ei1', '72.fu1', '72.fw1', '72.fy1', '72.gk1', '108.g1', '108.bd1', '108.bg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39916800, 1174645, 1174320, 268280812800, 6227827207, 7, 104], 'label': '46656.ir.36.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713839
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.l1', '432.o1', '432.bq1', '648.bu1'], 'contains': ['2592.d1', '2592.dn1', '2592.en1', '3888.l1', '3888.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [325, 355419187304, 40320, 39957127], 'label': '46656.ir.1296.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '1296.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.t1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713840
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.n1', '432.o1', '432.bs1', '648.z1', '648.bn1', '648.bv1'], 'contains': ['2592.f1', '2592.do1', '2592.ep1', '3888.l1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [325, 40320, 39957127, 104], 'label': '46656.ir.1296.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '1296.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.u1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713841
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.p1', '432.q1', '432.r1', '432.bt1', '648.g1', '648.u1', '648.be1'], 'contains': ['2592.c1', '2592.ds1', '2592.fr1', '3888.o1', '3888.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39366316080, 39916800, 6227827207, 104], 'label': '46656.ir.1296.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713842
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.p1', '432.bv1', '648.a1', '648.v1', '648.bg1'], 'contains': ['2592.h1', '2592.dv1', '2592.ft1', '3888.o1', '3888.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800, 6227827207], 'label': '46656.ir.1296.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.w1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713843
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.p1', '432.q1', '432.bu1', '648.w1'], 'contains': ['2592.i1', '2592.ea1', '2592.fw1', '3888.o1', '3888.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [39366316080, 1481684504, 39916800, 6227827207], 'label': '46656.ir.1296.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '1296.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713844
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.p1', '432.s1', '432.bw1', '648.h1', '648.q1', '648.be1'], 'contains': ['2592.c1', '2592.eb1', '2592.ga1', '3888.p1', '3888.q1', '3888.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40323593624, 39916800, 40323593520, 6227827207], 'label': '46656.ir.1296.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '1296.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.y1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713845
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.q1', '432.s1', '432.bx1', '648.r1'], 'contains': ['2592.e1', '2592.ec1', '2592.gd1', '3888.p1', '3888.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 325, 39916800, 6227827207], 'label': '46656.ir.1296.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '1296.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.z1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713846
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.r1', '432.s1', '432.by1', '648.k1', '648.s1', '648.ba1'], 'contains': ['2592.f1', '2592.ef1', '2592.gg1', '3888.p1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [325, 39916800, 6227827207, 104], 'label': '46656.ir.1296.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '1296.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ba1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713847
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.t1', '432.u1', '432.w1', '432.cc1', '648.i1', '648.bt1', '648.dg1'], 'contains': ['2592.b1', '2592.el1', '2592.ex1', '3888.s1', '3888.t1', '3888.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1134000, 39957127, 37885034880, 31658054835], 'label': '46656.ir.1296.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '1296.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713848
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.u1', '432.v1', '432.x1', '432.bz1', '648.j1', '648.q1', '648.u1'], 'contains': ['2592.c1', '2592.em1', '2592.ez1', '3888.s1', '3888.u1', '3888.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [387037284480, 1134000, 39957127, 435], 'label': '46656.ir.1296.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713849
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.e1'], 'contains': ['72.u1', '72.w1', '72.z1', '72.dy1', '72.dz1', '72.ej1', '72.ek1', '108.j1', '108.bi1', '324.bn1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1481684400, 39957120, 1134000, 499, 7, 301891126320, 325, 1521641624], 'label': '46656.ir.36.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713850
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.t1', '432.v1', '432.w1', '432.cb1', '648.bu1'], 'contains': ['2592.d1', '2592.en1', '2592.fa1', '3888.s1', '3888.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [325, 37885034984, 1134000, 39957127], 'label': '46656.ir.1296.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.bu1', 'old_label': '1296.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bd1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713851
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.t1', '432.v1', '432.x1', '432.ca1', '648.r1'], 'contains': ['2592.e1', '2592.eo1', '2592.fc1', '3888.s1', '3888.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [293708217704, 325, 1134000, 39957127], 'label': '46656.ir.1296.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.r1', 'old_label': '1296.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.be1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713852
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.w1', '432.x1', '432.cd1', '648.l1', '648.s1', '648.bj1', '648.bv1'], 'contains': ['2592.f1', '2592.ep1', '2592.fd1', '3888.s1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [325, 1134000, 39957127, 104], 'label': '46656.ir.1296.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bf1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713853
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.t1', '432.u1', '432.cg1', '648.dh1'], 'contains': ['2592.g1', '2592.eq1', '2592.ff1', '3888.t1', '3888.v1', '3888.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [299935198515, 1134000, 39957127, 37885034880], 'label': '46656.ir.1296.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '1296.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713854
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.u1', '432.ch1', '648.b1', '648.v1', '648.bk1', '648.di1'], 'contains': ['2592.h1', '2592.er1', '2592.fh1', '3888.t1', '3888.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [268280812800, 1134000, 39957127, 37885034880], 'label': '46656.ir.1296.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bh1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713855
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.u1', '432.v1', '432.ce1', '648.w1'], 'contains': ['2592.i1', '2592.es1', '2592.fm1', '3888.u1', '3888.v1', '3888.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [387037284480, 268280812904, 1134000, 39957127], 'label': '46656.ir.1296.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '1296.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713856
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.t1', '432.v1', '432.cf1'], 'contains': ['2592.j1', '2592.et1', '2592.fp1', '3888.v1', '3888.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [380810304104, 1134000, 39957127, 37885035205], 'label': '46656.ir.1296.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.bj1', 'old_label': '1296.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bj1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713857
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.t1', '432.v1', '432.cf2', '648.bl1'], 'contains': ['2592.j2', '2592.et2', '2592.fp2', '3888.v1', '3888.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [293708217925, 37885034984, 1134000, 39957127], 'label': '46656.ir.1296.bj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.bl1', 'old_label': '1296.bj2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bj2', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713858
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.y1', '432.cj1', '648.bm1', '648.bo1', '648.bs1', '648.bt1', '648.bw1', '648.by1', '648.dj1'], 'contains': ['2592.b1', '2592.cf1', '3888.x1', '3888.y1', '3888.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 1481684400, 39916800, 1521641624], 'label': '46656.ir.1296.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1296.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216713859
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.y1', '432.ci1', '648.bp1', '648.bu1', '648.bz1'], 'contains': ['2592.d1', '2592.cg1', '3888.x1', '3888.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1481684725, 39957120, 39957224, 39916800], 'label': '46656.ir.1296.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '1296.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713860
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '18.e1'], 'contains': ['72.u1', '72.x1', '72.y1', '72.ea1', '72.eb1', '72.el1', '72.em1', '108.k1', '108.bl1', '324.bo1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39916800, 1174645, 1174320, 268280812800, 7, 6227827818, 104], 'label': '46656.ir.36.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713861
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.cz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.y1', '432.ck1', '648.bn1', '648.bq1', '648.br1', '648.bv1', '648.bx1', '648.ca1', '648.cx1'], 'contains': ['2592.f1', '2592.ch1', '3888.x1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 325, 39957224, 39916800], 'label': '46656.ir.1296.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bm1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216713862
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.z1', '432.ba1', '648.cb1', '648.cc1', '648.cd1', '648.cf1', '648.cg1', '648.ch1', '648.ci1'], 'contains': ['2592.l1', '2592.p1', '2592.di1', '3888.b1', '3888.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 39916800], 'label': '46656.ir.1296.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713863
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.z1', '432.bb1', '648.ce1', '648.cj1', '648.ck1', '648.cl1', '648.cm1', '648.de1', '648.dk1'], 'contains': ['2592.o1', '2592.q1', '2592.dk1', '3888.a1', '3888.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 7, 39916800, 37885034880], 'label': '46656.ir.1296.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '1296.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713864
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ba1', '432.bb1', '432.bc1', '648.cn1', '648.co1', '648.df1'], 'contains': ['2592.k1', '2592.u1', '2592.dm1', '3888.c1', '3888.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [355419187635, 268280812800, 7, 39916800], 'label': '46656.ir.1296.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '1296.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713865
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ht1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bd1', '432.be1', '432.bf1', '432.bg1', '648.cn1', '648.cp1', '648.cs1'], 'contains': ['2592.k1', '2592.y1', '2592.cs1', '3888.d1', '3888.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [268280812800, 39916800, 6227827200, 355419187304], 'label': '46656.ir.1296.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '1296.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713866
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.fs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bd1', '432.bi1', '648.cb1', '648.cq1', '648.cu1'], 'contains': ['2592.l1', '2592.bf1', '2592.cw1', '3888.e1', '3888.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 39916800, 6227827200], 'label': '46656.ir.1296.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713867
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bd1', '432.be1', '432.bh1', '648.cr1'], 'contains': ['2592.n1', '2592.bg1', '2592.cx1', '3888.f1', '3888.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 39916800, 6227827200, 387999647384], 'label': '46656.ir.1296.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '1296.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713868
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bg1', '432.bh1', '432.bi1', '648.cc1', '648.ct1', '648.cu1'], 'contains': ['2592.l1', '2592.bm1', '2592.dc1', '3888.g1', '3888.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 39916800, 40323593520, 6227827200], 'label': '46656.ir.1296.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '1296.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713869
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bj1', '432.bk1', '432.bl1', '648.co1', '648.cs1', '648.cy1', '648.cz1', '648.da1', '648.db1', '648.dj1'], 'contains': ['2592.k1', '2592.bx1', '2592.cf1', '3888.h1', '3888.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1521641955, 39957120, 1481684400, 1134000], 'label': '46656.ir.1296.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1296.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713870
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ha1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bk1', '432.bm1', '648.cd1', '648.cu1', '648.dd1'], 'contains': ['2592.l1', '2592.cc1', '2592.ck1', '3888.j1', '3888.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 1481684400, 1134000], 'label': '46656.ir.1296.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713871
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.k1'], 'contains': ['72.v1', '72.ba1', '72.bd1', '72.ec1', '72.ee1', '72.en1', '72.eo1', '108.h1', '108.bi1', '324.bp1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 1134000, 499, 7, 325, 1521641624], 'label': '46656.ir.36.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '36.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713872
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bl1', '432.bm1', '648.ce1', '648.dc1', '648.dq1'], 'contains': ['2592.o1', '2592.cd1', '2592.cm1', '3888.i1', '3888.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 1134000], 'label': '46656.ir.1296.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '1296.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713873
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bn1', '432.bo1', '432.bp1', '648.dc1', '648.de1', '648.dn1'], 'contains': ['2592.o1', '2592.df1', '2592.ek1', '3888.k1', '3888.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1481684400, 39916800, 269279866800, 39957127], 'label': '46656.ir.1296.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713874
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bn1', '432.bq1', '432.br1', '432.bs1', '648.cy1', '648.df1', '648.dg1'], 'contains': ['2592.k1', '2592.dg1', '2592.el1', '3888.l1', '3888.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40320, 39957127, 37885034880, 31658054835], 'label': '46656.ir.1296.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '1296.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.by1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713875
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bo1', '432.bq1', '432.br1', '648.dh1'], 'contains': ['2592.m1', '2592.dj1', '2592.eq1', '3888.n1', '3888.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [299935198515, 40320, 39957127, 37885034880], 'label': '46656.ir.1296.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.di1', 'old_label': '1296.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.bz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713876
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bp1', '432.br1', '648.dc1', '648.di1', '648.dk1'], 'contains': ['2592.o1', '2592.dk1', '2592.er1', '3888.m1', '3888.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 39916800, 39957127, 37885034880], 'label': '46656.ir.1296.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '1296.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ca1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713877
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bt1', '432.bu1', '432.bv1', '648.cb1', '648.ct1', '648.dd1'], 'contains': ['2592.l1', '2592.dp1', '2592.fs1', '3888.o1', '3888.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 39916800, 6227827207], 'label': '46656.ir.1296.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713878
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bt1', '432.bw1', '432.bx1', '432.by1', '648.cn1', '648.cp1', '648.cz1'], 'contains': ['2592.k1', '2592.dq1', '2592.fy1', '3888.p1', '3888.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [355419187635, 268280812800, 39916800, 6227827207], 'label': '46656.ir.1296.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713879
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bv1', '432.bw1', '648.cc1', '648.cq1', '648.dd1'], 'contains': ['2592.l1', '2592.dt1', '2592.gh1', '3888.q1', '3888.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 39916800, 40323593520, 6227827207], 'label': '46656.ir.1296.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713880
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bu1', '432.bw1', '432.bx1', '648.cr1'], 'contains': ['2592.n1', '2592.du1', '2592.gi1', '3888.r1', '3888.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 268280812800, 39916800, 6227827207], 'label': '46656.ir.1296.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '1296.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ce1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713881
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bz1', '432.ca1', '432.cb1', '432.cc1', '432.cd1', '648.co1', '648.cp1', '648.dg1'], 'contains': ['2592.k1', '2592.eg1', '2592.ex1', '3888.s1', '3888.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1481684400, 1481684504, 1134000, 39957127], 'label': '46656.ir.1296.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713882
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.h1', '12.i1', '12.j1', '12.bs1', '12.bt1', '12.bv1', '12.bw1', '18.d1', '54.i1', '54.p1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6267381127, 7, 39957619, 269279866800], 'label': '46656.ir.6.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216713883
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '18.k1'], 'contains': ['72.v1', '72.bb1', '72.bc1', '72.ed1', '72.ee1', '72.ep1', '72.eq1', '108.i1', '108.bk1', '324.bq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 1134000, 7, 41051299, 325, 1521641624], 'label': '46656.ir.36.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '36.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713884
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.bz1', '432.ce1', '432.ch1', '648.cd1', '648.cq1', '648.ct1'], 'contains': ['2592.l1', '2592.eh1', '2592.fe1', '3888.u1', '3888.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 1481684400, 1134000, 39957127], 'label': '46656.ir.1296.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713885
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.cb1', '432.cc1', '432.ce1', '432.cf1', '432.cf2', '432.cg1', '648.dh1'], 'contains': ['2592.m1', '2592.ei1', '2592.ff1', '3888.v1', '3888.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 1481684400, 1134000, 39957127], 'label': '46656.ir.1296.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '1296.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ch1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713886
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.bz1', '432.ca1', '432.ce1', '432.cf1', '432.cf2', '432.cg1', '648.cr1'], 'contains': ['2592.n1', '2592.ej1', '2592.fg1', '3888.w1', '3888.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [294706903784, 1481684400, 1134000, 39957127], 'label': '46656.ir.1296.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '1296.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ci1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713887
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cc1', '432.cg1', '432.ch1', '648.ce1', '648.di1', '648.dn1'], 'contains': ['2592.o1', '2592.ek1', '2592.fh1', '3888.t1', '3888.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 1134000, 39957127], 'label': '46656.ir.1296.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713888
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ci1', '432.cj1', '432.ck1', '432.cl1', '648.df1', '648.dg1', '648.dj1'], 'contains': ['2592.b1', '2592.k1', '2592.ci1', '3888.x1', '3888.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39957120, 31697931315, 39916800, 37885034880], 'label': '46656.ir.1296.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bn1', 'old_label': '1296.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713889
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ci1', '432.cj1', '432.cm1', '648.dh1'], 'contains': ['2592.g1', '2592.m1', '2592.cl1', '3888.z1', '3888.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1521641955, 39957120, 39916800, 37885034880], 'label': '46656.ir.1296.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '1296.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713890
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cj1', '432.cn1', '648.de1', '648.di1', '648.dq1'], 'contains': ['2592.h1', '2592.o1', '2592.cm1', '3888.y1', '3888.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 39916800], 'label': '46656.ir.1296.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '1296.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713891
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cl1', '432.cm1', '432.cn1', '648.dk1', '648.dl1', '648.dm1', '648.dn1', '648.do1', '648.dp1', '648.dq1'], 'contains': ['2592.o1', '2592.co1', '3888.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 39957120, 39916800, 37885034880], 'label': '46656.ir.1296.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1296.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713892
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.co1', '432.di1', '648.cb1', '648.dr1', '648.ds1', '648.dt1', '648.du1', '648.dv1', '648.em1'], 'contains': ['2592.p1', '2592.bf1', '2592.dp1', '3888.bh1', '3888.bi1', '3888.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 6227827207], 'label': '46656.ir.1296.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.co1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713893
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.co1', '432.dj1', '648.cc1', '648.dx1', '648.ea1', '648.eb1', '648.ec1', '648.ed1', '648.em1'], 'contains': ['2592.p1', '2592.bm1', '2592.dt1', '3888.bh1', '3888.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 7, 40323593520, 6227827207], 'label': '46656.ir.1296.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713894
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.l1', '18.p1'], 'contains': ['72.bj1', '72.bm1', '72.bp1', '72.gc1', '72.gf1', '72.gp1', '72.gq1', '108.l1', '108.bp1', '324.bw1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 39916800, 269279866800, 39957127], 'label': '46656.ir.36.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216713895
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.co1', '432.dk1', '648.a1', '648.dy1', '648.ee1', '648.ef1', '648.eg1', '648.eh1', '648.en1'], 'contains': ['2592.q1', '2592.bn1', '2592.dv1', '3888.bj1', '3888.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 6227827207], 'label': '46656.ir.1296.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713896
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.co1', '432.cp1', '432.dl1', '648.dz1', '648.ei1', '648.ej1'], 'contains': ['2592.r1', '2592.bo1', '2592.dw1', '3888.bi1', '3888.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.1296.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713897
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cp1', '432.dm1', '648.dw1', '648.ek1', '648.el1'], 'contains': ['2592.s1', '2592.bp1', '2592.dy1', '3888.bi1', '3888.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [624302466480, 300933848880, 7, 6227827207], 'label': '46656.ir.1296.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1296.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713898
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cq1', '432.dn1', '648.dw1', '648.eo1', '648.ep1'], 'contains': ['2592.s1', '2592.ca1', '2592.ev1', '3888.bm1', '3888.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 301891126320, 7, 655477406640], 'label': '46656.ir.1296.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1296.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ct1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713899
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cr1', '432.do1', '648.cd1', '648.dr1', '648.dx1', '648.eq1', '648.er1', '648.es1', '648.et1'], 'contains': ['2592.p1', '2592.cc1', '2592.fe1', '3888.bn1', '3888.bo1', '3888.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 7, 269279866800, 37885034880], 'label': '46656.ir.1296.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713900
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cr1', '432.dp1', '648.b1', '648.ce1', '648.dy1', '648.eu1', '648.ev1', '648.ew1', '648.ex1'], 'contains': ['2592.q1', '2592.cd1', '2592.fh1', '3888.bn1', '3888.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 37885034880], 'label': '46656.ir.1296.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cv1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713901
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cq1', '432.cr1', '432.dq1', '648.dz1', '648.ey1', '648.ez1'], 'contains': ['2592.r1', '2592.ce1', '2592.fi1', '3888.bo1', '3888.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 269279866800], 'label': '46656.ir.1296.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '1296.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cw1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713902
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cs1', '432.dr1', '648.cd1', '648.em1', '648.fa1', '648.fb1', '648.fc1', '648.fd1', '648.fe1'], 'contains': ['2592.p1', '2592.ck1', '2592.eh1', '3888.bq1', '3888.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 39957120, 7, 1481684400], 'label': '46656.ir.1296.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713903
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cs1', '432.ds1', '648.ce1', '648.de1', '648.ff1', '648.fg1', '648.fh1', '648.fi1', '648.fu1'], 'contains': ['2592.q1', '2592.cm1', '2592.ek1', '3888.bq1', '3888.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400], 'label': '46656.ir.1296.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713904
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cs1', '432.dt1', '648.b1', '648.dk1', '648.en1', '648.fj1', '648.fk1', '648.fl1', '648.fm1', '648.fn1', '648.fo1', '648.fp1', '648.fq1', '648.fr1', '648.fs1', '648.ft1', '648.fu1'], 'contains': ['2592.q1', '2592.co1', '2592.er1', '3888.br1', '3888.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 37885034880], 'label': '46656.ir.1296.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1296.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.cz1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713905
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.m1', '18.p1'], 'contains': ['72.bm1', '72.bn1', '72.bo1', '72.gw1', '72.gx1', '72.ha1', '72.hd1', '108.m1', '108.bs1', '324.cb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 39916800, 6227827207, 39957127, 269279866800], 'label': '46656.ir.36.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216713906
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ct1', '432.du1', '648.cb1', '648.dx1', '648.fa1', '648.fv1', '648.fw1', '648.fx1', '648.fy1'], 'contains': ['2592.p1', '2592.cw1', '2592.fs1', '3888.bt1', '3888.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7], 'label': '46656.ir.1296.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.da1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713907
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ct1', '432.dv1', '648.a1', '648.dy1', '648.fj1', '648.fz1', '648.ga1', '648.gb1', '648.gc1'], 'contains': ['2592.q1', '2592.cy1', '2592.ft1', '3888.bt1', '3888.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1481684400], 'label': '46656.ir.1296.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.db1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713908
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ct1', '432.cu1', '432.cv1', '432.dw1', '648.dz1', '648.gd1', '648.ge1'], 'contains': ['2592.r1', '2592.cz1', '2592.fu1', '3888.bt1', '3888.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 269279866800], 'label': '46656.ir.1296.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '1296.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713909
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ct1', '432.dx1', '648.cc1', '648.dr1', '648.fa1', '648.gf1', '648.gg1', '648.gh1', '648.gi1'], 'contains': ['2592.p1', '2592.dc1', '2592.gh1', '3888.bu1', '3888.bv1', '3888.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 40323593520], 'label': '46656.ir.1296.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713910
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cu1', '432.dy1', '648.dw1', '648.gj1', '648.gk1'], 'contains': ['2592.s1', '2592.dd1', '2592.gk1', '3888.bv1', '3888.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 301891126320, 7, 655477406640], 'label': '46656.ir.1296.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '1296.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.de1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713911
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.cv1', '432.dz1', '648.gl1'], 'contains': ['2592.t1', '2592.de1', '2592.gm1', '3888.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 301891126320, 7, 623823424560], 'label': '46656.ir.1296.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '1296.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.df1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216713912
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.dr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cp1', '432.cw1', '648.cf1', '648.ds1', '648.ea1', '648.eq1', '648.fb1', '648.fv1', '648.gf1'], 'contains': ['2592.p1', '3888.by1', '3888.cg1', '3888.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [31658054844, 499, 269279866800, 37885034880], 'label': '46656.ir.1296.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713913
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cq1', '432.cx1', '648.cf1', '648.dt1', '648.eb1', '648.er1', '648.fc1', '648.fw1', '648.gg1'], 'contains': ['2592.p1', '3888.ca1', '3888.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39917299, 39366316080, 268280812800, 444], 'label': '46656.ir.1296.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713914
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cr1', '432.cy1', '648.cg1', '648.ds1', '648.ec1', '648.es1', '648.fd1', '648.fw1', '648.gh1'], 'contains': ['2592.p1', '3888.cb1', '3888.ch1', '3888.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 268280812800, 6227827818], 'label': '46656.ir.1296.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.di1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216713915
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cs1', '432.cy1', '648.ch1', '648.du1', '648.ea1', '648.et1', '648.fd1', '648.fx1', '648.gg1'], 'contains': ['2592.p1', '3888.cb1', '3888.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 268280812800, 6227827818, 40323593520], 'label': '46656.ir.1296.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713916
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '18.k1'], 'contains': ['72.f1', '72.g1', '72.ba1', '72.bb1', '72.bq1', '72.en1', '72.ep1', '108.p1', '108.bt1', '324.cc1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 39916800, 499, 7, 325, 1521641624], 'label': '46656.ir.36.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '36.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216713917
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ct1', '432.cz1', '648.ci1', '648.dv1', '648.ed1', '648.eq1', '648.fc1', '648.fx1', '648.gh1'], 'contains': ['2592.p1', '3888.cc1', '3888.ci1', '3888.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 41091619, 269279866800, 37885034880], 'label': '46656.ir.1296.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713918
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cu1', '432.da1', '648.ci1', '648.du1', '648.ec1', '648.er1', '648.fb1', '648.fy1', '648.gi1'], 'contains': ['2592.p1', '3888.cd1', '3888.cp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 1481684400, 39957619, 1481684844], 'label': '46656.ir.1296.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713919
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cv1', '432.db1', '648.cg1', '648.dt1', '648.ed1', '648.et1', '648.fe1', '648.fv1', '648.gi1'], 'contains': ['2592.p1', '3888.cf1', '3888.cq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 268280812800, 6267744618], 'label': '46656.ir.1296.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713920
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cw1', '432.db1', '648.ch1', '648.dv1', '648.eb1', '648.es1', '648.fe1', '648.fy1', '648.gf1'], 'contains': ['2592.p1', '3888.cf1', '3888.cj1', '3888.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 268280812800, 6267744618, 40323593520], 'label': '46656.ir.1296.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713921
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cx1', '432.cw1', '648.c1', '648.cj1', '648.ee1', '648.eu1', '648.ff1', '648.fk1', '648.fz1'], 'contains': ['2592.q1', '3888.by1', '3888.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [31658054844, 268280812800, 499, 37885034880], 'label': '46656.ir.1296.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1296.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.do1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216713922
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cy1', '432.cx1', '648.c1', '648.ck1', '648.ef1', '648.ev1', '648.fh1', '648.fm1', '648.ga1'], 'contains': ['2592.q1', '3888.bz1', '3888.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39917299, 39366316080, 1481684400, 1481684844], 'label': '46656.ir.1296.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dp1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216713923
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.cz1', '432.cx1', '648.d1', '648.cj1', '648.cl1', '648.ew1', '648.fg1', '648.fh1', '648.fn1'], 'contains': ['2592.q1', '3888.bz1', '3888.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [31658054844, 39917299, 268280812800, 37885034880], 'label': '46656.ir.1296.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '1296.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713924
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.da1', '432.cy1', '648.e1', '648.ee1', '648.eg1', '648.ex1', '648.fp1', '648.ga1', '648.gb1'], 'contains': ['2592.q1', '3888.cm1', '3888.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 39366316080, 1481684400, 6227827818], 'label': '46656.ir.1296.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713925
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.db1', '432.cz1', '648.f1', '648.cm1', '648.eh1', '648.eu1', '648.fg1', '648.fm1', '648.gb1'], 'contains': ['2592.q1', '3888.cc1', '3888.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [31658054844, 41091619, 268280812800, 37885034880], 'label': '46656.ir.1296.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ds1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713926
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dc1', '432.da1', '648.d1', '648.ck1', '648.cm1', '648.ew1', '648.ff1', '648.fi1', '648.fq1'], 'contains': ['2592.q1', '3888.cd1', '3888.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957619, 1481684844], 'label': '46656.ir.1296.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713927
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.k1'], 'contains': ['72.g1', '72.i1', '72.bc1', '72.bd1', '72.bq1', '72.eo1', '72.eq1', '108.q1', '108.bu1', '324.cd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 39916800, 7, 41051299, 325, 1521641624], 'label': '46656.ir.36.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '36.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216713928
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dd1', '432.da1', '648.f1', '648.cl1', '648.eg1', '648.ev1', '648.fi1', '648.fk1', '648.gc1'], 'contains': ['2592.q1', '3888.ce1', '3888.cp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [31658054844, 268280812800, 39957619, 37885034880], 'label': '46656.ir.1296.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1296.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.du1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216713929
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.de1', '432.db1', '648.e1', '648.ef1', '648.eh1', '648.ex1', '648.fr1', '648.fz1', '648.gc1'], 'contains': ['2592.q1', '3888.cq1', '3888.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 6267744618, 1481684400], 'label': '46656.ir.1296.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713930
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.df1', '432.cw1', '432.dc1', '432.dg1', '648.ei1', '648.ey1', '648.gd1'], 'contains': ['2592.r1', '3888.cg1', '3888.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 499, 444, 269279866800], 'label': '46656.ir.1296.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '1296.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713931
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dg1', '432.cy1', '432.dd1', '648.ei1', '648.ez1', '648.ge1'], 'contains': ['2592.r1', '3888.ch1', '3888.cn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [469, 6227827818, 40323593520, 269279866800], 'label': '46656.ir.1296.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '1296.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713932
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dh1', '432.cz1', '432.de1', '648.ej1', '648.ey1', '648.ge1'], 'contains': ['2592.r1', '3888.ci1', '3888.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091619, 39366316080, 444, 269279866800], 'label': '46656.ir.1296.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '1296.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dy1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714312
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ge1', '486.t1', '648.el1', '972.cg1'], 'contains': ['3888.bl1', '3888.cu1', '3888.cv1', '5832.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091619, 93576273840, 444, 6227389164], 'label': '46656.ir.1944.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '1944.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216713933
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.di1', '432.db1', '432.df1', '432.dh1', '648.ej1', '648.ez1', '648.gd1'], 'contains': ['2592.r1', '3888.cj1', '3888.cq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [469, 39366316080, 6267744618, 269279866800], 'label': '46656.ir.1296.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '1296.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713934
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dj1', '432.dc1', '648.ek1', '648.eo1', '648.gj1'], 'contains': ['2592.s1', '3888.cg1', '3888.cs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [301891126320, 499, 655477406640, 444], 'label': '46656.ir.1296.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '1296.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ea1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713935
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dk1', '432.dd1', '648.ek1', '648.ep1', '648.gk1'], 'contains': ['2592.s1', '3888.ch1', '3888.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [469, 624302466480, 300933848880, 6227827818], 'label': '46656.ir.1296.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1296.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713936
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dl1', '432.de1', '648.el1', '648.eo1', '648.gk1'], 'contains': ['2592.s1', '3888.ci1', '3888.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091619, 301891126320, 655477406640, 444], 'label': '46656.ir.1296.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1296.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ec1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713937
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dm1', '432.df1', '648.el1', '648.ep1', '648.gj1'], 'contains': ['2592.s1', '3888.cj1', '3888.cv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [469, 301891126320, 6267744618, 655477406640], 'label': '46656.ir.1296.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '1296.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ed1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216713938
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.n1', '18.p1'], 'contains': ['72.bs1', '72.bv1', '72.cc1', '72.ct1', '72.cw1', '72.gc1', '72.gw1', '108.by1', '108.ce1', '324.v1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 6227827207, 7, 269279866800, 40320], 'label': '46656.ir.36.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216713939
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.dn1', '432.dg1', '648.gl1'], 'contains': ['2592.t1', '3888.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [301891126320, 499, 444, 623823424560], 'label': '46656.ir.1296.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '1296.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ee1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 216713940
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.do1', '432.dh1', '648.gl1'], 'contains': ['2592.t1', '3888.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [469, 301891126320, 6267744618, 623823424560], 'label': '46656.ir.1296.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '1296.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ef1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216713941
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.di1', '432.dj1', '432.ea1', '648.cn1', '648.gm1', '648.gp1'], 'contains': ['2592.u1', '2592.y1', '2592.dq1', '3888.bh1', '3888.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [355419187635, 268280812800, 7, 6227827207], 'label': '46656.ir.1296.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713942
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.di1', '432.dl1', '432.dm1', '432.eb1', '648.gn1'], 'contains': ['2592.v1', '2592.z1', '2592.dr1', '3888.bi1', '3888.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387999647280, 7, 387999647715, 6227827207], 'label': '46656.ir.1296.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ex1', 'old_label': '1296.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713943
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.di1', '432.dk1', '432.ec1', '648.g1', '648.go1', '648.gs1'], 'contains': ['2592.w1', '2592.ba1', '2592.ds1', '3888.bj1', '3888.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 7, 6227827207, 435], 'label': '46656.ir.1296.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ei1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713944
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dj1', '432.dk1', '432.dl1', '432.ed1', '648.h1', '648.gr1', '648.gs1'], 'contains': ['2592.w1', '2592.bk1', '2592.eb1', '3888.bk1', '3888.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 7, 40323593520, 6227827207], 'label': '46656.ir.1296.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '1296.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ej1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713945
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.eb1', '432.dm1', '432.ee1', '648.gq1'], 'contains': ['2592.x1', '2592.bl1', '2592.ed1', '3888.bl1', '3888.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [623710972161, 7, 6227827207, 104], 'label': '46656.ir.1296.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '1296.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ek1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713946
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bs1', '432.dn1', '432.ef1', '648.gq1'], 'contains': ['2592.x1', '2592.bu1', '2592.eu1', '3888.bm1', '3888.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [41091120, 7, 325, 93535994618], 'label': '46656.ir.1296.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '1296.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.el1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713947
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.do1', '432.dp1', '432.eg1', '648.i1', '648.co1', '648.gm1'], 'contains': ['2592.u1', '2592.bx1', '2592.ex1', '3888.bn1', '3888.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 7, 37885034880, 31658054835], 'label': '46656.ir.1296.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.em1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713948
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dn1', '432.do1', '432.dq1', '432.eh1', '648.gn1'], 'contains': ['2592.v1', '2592.by1', '2592.ey1', '3888.bo1', '3888.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 301891126320, 7, 435], 'label': '46656.ir.1296.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '1296.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.en1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713949
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.o1', '18.p1'], 'contains': ['72.bs1', '72.by1', '72.cf1', '72.cv1', '72.cx1', '72.gp1', '72.gx1', '108.bz1', '108.cf1', '324.w1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 7, 269279866800, 40320], 'label': '46656.ir.36.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216713950
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.do1', '432.dp1', '432.dq1', '432.ei1', '648.j1', '648.go1', '648.gr1'], 'contains': ['2592.w1', '2592.bz1', '2592.ez1', '3888.bp1', '3888.cx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 104], 'label': '46656.ir.1296.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713951
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dr1', '432.ds1', '432.ej1', '648.bm1', '648.co1', '648.gp1', '648.gt1', '648.gu1', '648.gv1', '648.gy1'], 'contains': ['2592.u1', '2592.cf1', '2592.eg1', '3888.bq1', '3888.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1521641955, 39957120, 7, 1481684400], 'label': '46656.ir.1296.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ep1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713952
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ds1', '432.dt1', '432.ek1', '648.i1', '648.df1', '648.gy1'], 'contains': ['2592.u1', '2592.ci1', '2592.el1', '3888.br1', '3888.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39957120, 7, 31697930984, 37885034880], 'label': '46656.ir.1296.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '1296.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713953
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dr1', '432.dt1', '432.el1', '648.j1', '648.gs1', '648.gw1'], 'contains': ['2592.w1', '2592.cj1', '2592.em1', '3888.bs1', '3888.cy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [387037284480, 39957120, 7, 39957224], 'label': '46656.ir.1296.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.er1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713954
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.du1', '432.dv1', '432.dw1', '432.em1', '648.g1', '648.gr1', '648.gw1'], 'contains': ['2592.w1', '2592.cp1', '2592.fr1', '3888.bt1', '3888.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 435], 'label': '46656.ir.1296.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.es1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713955
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.du1', '432.dx1', '432.en1', '648.cn1', '648.gm1', '648.gt1'], 'contains': ['2592.u1', '2592.cs1', '2592.fy1', '3888.bu1', '3888.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 355419187635, 268280812800, 7], 'label': '46656.ir.1296.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.et1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713956
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dw1', '432.dx1', '432.dy1', '432.dz1', '432.eo1', '648.gn1'], 'contains': ['2592.v1', '2592.ct1', '2592.fz1', '3888.bv1', '3888.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 301891126320, 7, 104], 'label': '46656.ir.1296.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '1296.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.eu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713957
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.dv1', '432.dx1', '432.ep1', '648.h1', '648.go1', '648.gw1'], 'contains': ['2592.w1', '2592.cu1', '2592.ga1', '3888.bw1', '3888.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40323593624, 6267744007, 7, 40323593520], 'label': '46656.ir.1296.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '1296.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ev1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713958
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.ec1', '432.dy1', '432.eq1', '648.gq1'], 'contains': ['2592.x1', '2592.cv1', '2592.ge1', '3888.bx1', '3888.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 7, 325, 655807627898], 'label': '46656.ir.1296.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '1296.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ew1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713959
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ea1', '432.eb1', '432.ec1', '432.ed1', '432.ee1', '648.k1', '648.gz1', '648.ha1', '648.hb1', '648.hc1', '648.hd1', '648.he1'], 'contains': ['2592.a1', '2592.be1', '2592.ef1', '3888.cw1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7, 325, 6227827207, 104], 'label': '46656.ir.1296.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ex1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713960
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '18.f1', '18.g1', '18.j1'], 'contains': ['72.bt1', '72.bw1', '72.cd1', '72.dv1', '72.et1', '72.gd1', '72.gy1', '108.ce1', '324.x1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 7, 40320], 'label': '46656.ir.36.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713961
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ef1', '432.eg1', '432.eh1', '432.ei1', '648.l1', '648.gz1', '648.hf1', '648.hg1', '648.hh1'], 'contains': ['2592.a1', '2592.bw1', '2592.fd1', '3888.cx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 7, 325, 104], 'label': '46656.ir.1296.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1296.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ey1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713962
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ej1', '432.ek1', '432.el1', '648.l1', '648.bn1', '648.he1', '648.hi1', '648.hj1', '648.hk1', '648.hl1', '648.hm1', '648.hn1', '648.ho1', '648.hp1', '648.hq1', '648.hr1', '648.hs1', '648.ht1'], 'contains': ['2592.a1', '2592.ch1', '2592.ep1', '3888.cy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 7, 325, 39957224], 'label': '46656.ir.1296.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ez1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713963
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.em1', '432.en1', '432.eo1', '432.ep1', '432.eq1', '648.k1', '648.gz1', '648.hi1', '648.hu1', '648.hv1', '648.hw1', '648.hx1'], 'contains': ['2592.a1', '2592.cr1', '2592.gg1', '3888.cz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 7, 325, 104], 'label': '46656.ir.1296.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '1296.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fa1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713964
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.es1', '432.et1', '432.fe1', '648.m1', '648.n1', '648.hb1', '648.hg1', '648.hl1', '648.hm1', '648.hv1'], 'contains': ['2592.a1', '11664.m1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39917299, 7, 325, 104], 'label': '46656.ir.1296.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1296.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fb1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713965
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.eu1', '432.fa1', '432.ff1', '432.fg1', '432.fm1', '648.o1', '648.ha1', '648.hc1', '648.hh1', '648.ho1', '648.hv1', '648.hw1'], 'contains': ['2592.a1', '11664.n1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7, 325, 6227827818, 104], 'label': '46656.ir.1296.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fc1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713966
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ev1', '432.fb1', '432.fh1', '432.fn1', '648.p1', '648.hd1', '648.hf1', '648.hl1', '648.hw1'], 'contains': ['2592.a1', '11664.o1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091619, 7, 325, 104], 'label': '46656.ir.1296.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1296.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fd1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713967
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ew1', '432.ex1', '432.fi1', '648.n1', '648.p1', '648.hc1', '648.hg1', '648.hj1', '648.hp1', '648.hx1'], 'contains': ['2592.a1', '11664.p1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 325, 39957619, 104], 'label': '46656.ir.1296.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fe1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713968
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ey1', '432.fc1', '432.fj1', '432.fk1', '432.fo1', '648.o1', '648.hb1', '648.hd1', '648.hh1', '648.hq1', '648.hu1', '648.hx1'], 'contains': ['2592.a1', '11664.q1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744618, 7, 325, 104], 'label': '46656.ir.1296.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '1296.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ff1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713969
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fp1', '432.fq1', '432.fr1', '432.gj1', '432.gk1', '648.t1', '648.gz1', '648.hy1'], 'contains': ['2592.be1', '2592.bw1', '2592.cr1', '3888.da1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 325, 6227827200, 104], 'label': '46656.ir.1296.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fg1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216713970
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fp1', '432.fs1', '432.gm1', '648.cs1', '648.gm1', '648.ia1'], 'contains': ['2592.y1', '2592.bx1', '2592.cs1', '3888.da1', '3888.db1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 355419187635, 268280812800, 6227827200], 'label': '46656.ir.1296.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bg1', 'old_label': '1296.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713971
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '18.h1', '18.i1', '18.j1'], 'contains': ['72.bt1', '72.bx1', '72.cg1', '72.er1', '72.ew1', '72.gm1', '72.gz1', '108.cf1', '324.y1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 7, 40320], 'label': '46656.ir.36.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713972
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fq1', '432.fs1', '432.gl1', '432.go1', '648.gn1'], 'contains': ['2592.z1', '2592.by1', '2592.ct1', '3888.da1', '3888.dc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 387999647280, 6227827200, 387999647384], 'label': '46656.ir.1296.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fk1', 'old_label': '1296.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713973
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fr1', '432.fs1', '432.gn1', '648.x1', '648.go1', '648.hz1'], 'contains': ['2592.ba1', '2592.bz1', '2592.cu1', '3888.da1', '3888.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 39366316080, 6227827200, 104], 'label': '46656.ir.1296.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '1296.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713974
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ha1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fs1', '432.gp1', '648.cu1', '648.dr1', '648.ib1'], 'contains': ['2592.bf1', '2592.cc1', '2592.dc1', '3888.db1', '3888.dc1', '3888.dd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 6227827200], 'label': '46656.ir.1296.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713975
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ft1', '432.fu1', '432.fv1', '432.gq1', '648.g1', '648.hz1', '648.ip1'], 'contains': ['2592.ba1', '2592.dh1', '2592.fr1', '3888.de1', '3888.df1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 39366316080, 6227827200, 435], 'label': '46656.ir.1296.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713976
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ft1', '432.gs1', '648.cb1', '648.ib1', '648.iq1'], 'contains': ['2592.bf1', '2592.di1', '2592.fs1', '3888.de1', '3888.dg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 6227827200], 'label': '46656.ir.1296.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713977
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ft1', '432.fu1', '432.gr1', '648.ir1'], 'contains': ['2592.bi1', '2592.dl1', '2592.fv1', '3888.de1', '3888.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812904, 6227827200], 'label': '46656.ir.1296.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '1296.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713978
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ft1', '432.fw1', '432.gt1', '648.cn1', '648.ia1', '648.id1'], 'contains': ['2592.y1', '2592.dm1', '2592.fy1', '3888.df1', '3888.dg1', '3888.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 355419187635, 268280812800, 6227827200], 'label': '46656.ir.1296.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713979
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fu1', '432.fw1', '432.gu1', '648.ie1'], 'contains': ['2592.bb1', '2592.dn1', '2592.gb1', '3888.df1', '3888.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39916807, 325, 6227827200, 355419187304], 'label': '46656.ir.1296.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '1296.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fp1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713980
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fv1', '432.fw1', '432.gv1', '648.k1', '648.hy1', '648.if1'], 'contains': ['2592.be1', '2592.do1', '2592.gg1', '3888.df1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 325, 6227827200, 104], 'label': '46656.ir.1296.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '1296.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fq1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713981
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fx1', '432.fy1', '432.fz1', '432.gw1', '648.cp1', '648.gp1', '648.ia1'], 'contains': ['2592.y1', '2592.dq1', '2592.eg1', '3888.di1', '3888.dj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [355419187635, 1174327, 268280812800, 6227827207], 'label': '46656.ir.1296.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '1296.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713982
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '18.f1', '18.h1', '18.k1'], 'contains': ['72.ba1', '72.bc1', '72.bt1', '72.es1', '72.ev1', '108.bt1', '324.cj1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39957120, 39916800, 268280812800, 37885034880, 499, 7, 325, 31697930984], 'label': '46656.ir.36.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713983
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fx1', '432.gy1', '648.cq1', '648.em1', '648.ib1'], 'contains': ['2592.bf1', '2592.dt1', '2592.eh1', '3888.di1', '3888.dk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 268280812800, 40323593520, 6227827207], 'label': '46656.ir.1296.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713984
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fx1', '432.fy1', '432.gx1', '648.cr1'], 'contains': ['2592.bg1', '2592.du1', '2592.ej1', '3888.di1', '3888.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 1174327, 268280812800, 6227827207], 'label': '46656.ir.1296.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '1296.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ft1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216713985
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fx1', '432.ga1', '432.gz1', '648.q1', '648.gs1', '648.hz1'], 'contains': ['2592.ba1', '2592.eb1', '2592.em1', '3888.dj1', '3888.dk1', '3888.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1174327, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.1296.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713986
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.fy1', '432.ga1', '432.ha1', '648.r1'], 'contains': ['2592.bd1', '2592.ec1', '2592.eo1', '3888.dj1', '3888.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1174327, 40323593845, 6227827207, 104], 'label': '46656.ir.1296.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '1296.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fv1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713987
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fz1', '432.ga1', '432.hb1', '648.s1', '648.he1', '648.hy1'], 'contains': ['2592.be1', '2592.ef1', '2592.ep1', '3888.dj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 325, 6227827207, 104], 'label': '46656.ir.1296.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '1296.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fw1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713988
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gb1', '432.gc1', '432.gf1', '432.hf1', '648.cp1', '648.gm1', '648.id1'], 'contains': ['2592.y1', '2592.ex1', '2592.fy1', '3888.dm1', '3888.dn1', '3888.dq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [355419187635, 268280812800, 6227827200, 41091127], 'label': '46656.ir.1296.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '1296.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713989
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gb1', '432.gd1', '432.gg1', '432.hc1', '432.hh1', '648.gn1'], 'contains': ['2592.z1', '2592.ey1', '2592.fz1', '3888.dm1', '3888.do1', '3888.dr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [387999647280, 387999647715, 6227827200, 41091127], 'label': '46656.ir.1296.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gn1', 'old_label': '1296.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713990
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gb1', '432.ge1', '432.gh1', '432.hg1', '648.q1', '648.go1', '648.ip1'], 'contains': ['2592.ba1', '2592.ez1', '2592.ga1', '3888.dm1', '3888.dp1', '3888.ds1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39366316080, 6227827200, 41091127, 435], 'label': '46656.ir.1296.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.fz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713991
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gd1', '432.ge1', '432.gf1', '432.hi1', '648.ie1'], 'contains': ['2592.bb1', '2592.fa1', '2592.gb1', '3888.dm1', '3888.dq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [268280813125, 6227827200, 355419187304, 41091127], 'label': '46656.ir.1296.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ie1', 'old_label': '1296.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ga1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713992
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gc1', '432.gd1', '432.ge1', '432.gg1', '432.hd1', '432.hk1'], 'contains': ['2592.bc1', '2592.fb1', '2592.gc1', '3888.dm1', '3888.dr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [295664181224, 325, 6227827200, 41091127], 'label': '46656.ir.1296.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.gb1', 'old_label': '1296.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gb1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713993
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.n1', '12.p1', '12.r1', '12.bf1', '12.bh1', '12.bp1', '12.bs1', '18.f1', '54.b1', '54.t1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 499, 7, 40320, 269279866800], 'label': '46656.ir.6.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216713994
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '18.g1', '18.i1', '18.k1'], 'contains': ['72.bb1', '72.bd1', '72.bt1', '72.eu1', '72.ey1', '108.bu1', '324.ck1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39957120, 39916800, 268280812800, 37885034880, 7, 41051299, 325, 31697930984], 'label': '46656.ir.36.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216713995
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gc1', '432.gd1', '432.gh1', '432.hj1', '648.r1'], 'contains': ['2592.bd1', '2592.fc1', '2592.gd1', '3888.dm1', '3888.ds1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [34096648424, 39366316405, 6227827200, 41091127], 'label': '46656.ir.1296.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.r1', 'old_label': '1296.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216713996
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gf1', '432.gg1', '432.gh1', '432.he1', '432.hl1', '648.s1', '648.gz1', '648.if1'], 'contains': ['2592.be1', '2592.fd1', '2592.gg1', '3888.dm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [325, 6227827200, 104, 41091127], 'label': '46656.ir.1296.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gd1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216713997
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gb1', '432.ho1', '648.cq1', '648.dr1', '648.iq1'], 'contains': ['2592.bf1', '2592.fe1', '2592.gh1', '3888.dn1', '3888.do1', '3888.dp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827200, 41091127], 'label': '46656.ir.1296.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ge1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713998
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gb1', '432.gc1', '432.hm1', '648.cr1'], 'contains': ['2592.bg1', '2592.fg1', '2592.gi1', '3888.dn1', '3888.dr1', '3888.ds1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [268280812800, 387999647715, 6227827200, 41091127], 'label': '46656.ir.1296.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '1296.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216713999
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gb1', '432.gd1', '432.hp1'], 'contains': ['2592.bh1', '2592.fj1', '2592.gj1', '3888.do1', '3888.dq1', '3888.dr1', '3888.ds1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [382729979955, 387999647280, 6227827200, 41091127], 'label': '46656.ir.1296.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.gg1', 'old_label': '1296.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gg1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714000
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gb1', '432.ge1', '432.hn1', '648.ir1'], 'contains': ['2592.bi1', '2592.fl1', '2592.go1', '3888.dp1', '3888.dq1', '3888.dr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [268280813235, 39366316080, 6227827200, 41091127], 'label': '46656.ir.1296.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '1296.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714001
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gc1', '432.gd1', '432.ge1', '432.hq1'], 'contains': ['2592.bj1', '2592.fo2', '2592.gp1', '3888.dq1', '3888.dr1', '3888.ds1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [295664181445, 39366316184, 6227827200, 41091127], 'label': '46656.ir.1296.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.gi1', 'old_label': '1296.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gi1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714002
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gi2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['432.gc1', '432.gd1', '432.ge1', '432.hq2'], 'contains': ['2592.bj2', '2592.fo1', '2592.gp2', '3888.dq1', '3888.dr1', '3888.ds1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 5184, 'diagramx': None, 'generators': [39366316405, 6227827200, 355419187304, 41091127], 'label': '46656.ir.1296.gi2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.gi2', 'old_label': '1296.gi2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gi2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714003
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gi1', '432.hr1', '648.bo1', '648.cs1', '648.gp1', '648.ic1', '648.id1', '648.ih1', '648.il1'], 'contains': ['2592.y1', '2592.cf1', '3888.dt1', '3888.du1', '3888.dv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [355419187635, 268280812800, 1174320, 6227827200], 'label': '46656.ir.1296.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1296.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714004
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gi1', '432.hs1', '648.bp1', '648.ie1', '648.ii1'], 'contains': ['2592.bb1', '2592.cg1', '3888.dt1', '3888.dv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268281987445, 1174320, 6227827200, 355419187304], 'label': '46656.ir.1296.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '1296.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714005
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '18.f1', '18.i1', '18.l1'], 'contains': ['72.bt1', '72.ex1', '72.fa1', '324.bb1', '324.cl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6227827818, 40320], 'label': '46656.ir.36.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714006
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ca1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gi1', '432.ht1', '648.t1', '648.bq1', '648.he1', '648.if1', '648.ig1', '648.ij1', '648.ik1'], 'contains': ['2592.be1', '2592.ch1', '3888.dt1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174320, 6227827200, 104, 1174645], 'label': '46656.ir.1296.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gl1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714007
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bx1', '432.gj1', '432.gl1', '648.gq1'], 'contains': ['2592.bl1', '2592.bu1', '2592.cv1', '3888.da1', '3888.dw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 93536397441, 6227827200, 104], 'label': '46656.ir.1296.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fx1', 'old_label': '1296.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714008
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gk1', '432.gm1', '432.gn1', '432.go1', '648.x1', '648.gr1', '648.im1'], 'contains': ['2592.bk1', '2592.bz1', '2592.cp1', '3888.da1', '3888.dx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 40323593955, 40323593520, 6227827200], 'label': '46656.ir.1296.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '1296.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714009
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gl1', '432.hx1', '648.dw1'], 'contains': ['2592.bp1', '2592.ca1', '2592.dd1', '3888.dc1', '3888.dw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 300933848880, 6227827200, 93575951280], 'label': '46656.ir.1296.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '1296.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.go1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714010
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ha1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gm1', '432.gp1', '648.cu1', '648.dx1', '648.io1'], 'contains': ['2592.bm1', '2592.cc1', '2592.cw1', '3888.db1', '3888.dx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 268280812800, 40323593520, 6227827200], 'label': '46656.ir.1296.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714011
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gn1', '432.gp1', '648.y1', '648.dy1', '648.in1'], 'contains': ['2592.bn1', '2592.cd1', '2592.cy1', '3888.dd1', '3888.dx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 6227827200], 'label': '46656.ir.1296.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '1296.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714012
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.go1', '432.gp1', '432.hx1', '648.dz1'], 'contains': ['2592.bo1', '2592.ce1', '2592.cz1', '3888.dc1', '3888.dx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.1296.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '1296.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714013
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gq1', '432.gr1', '432.gs1', '648.a1', '648.in1', '648.it1'], 'contains': ['2592.bn1', '2592.df1', '2592.ft1', '3888.de1', '3888.dy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 6227827200], 'label': '46656.ir.1296.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714014
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gq1', '432.gt1', '432.gu1', '432.gv1', '648.h1', '648.im1', '648.ip1'], 'contains': ['2592.bk1', '2592.dh1', '2592.ga1', '3888.df1', '3888.dy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 40323593955, 40323593520, 6227827200], 'label': '46656.ir.1296.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '1296.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714015
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gs1', '432.gt1', '648.cc1', '648.io1', '648.iq1'], 'contains': ['2592.bm1', '2592.di1', '2592.gh1', '3888.dg1', '3888.dy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 268280812800, 40323593520, 6227827200], 'label': '46656.ir.1296.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714016
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '18.g1', '18.h1', '18.l1'], 'contains': ['72.bt1', '72.ez1', '72.fb1', '324.bc1', '324.cm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6267381738, 40320], 'label': '46656.ir.36.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714017
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gr1', '432.gt1', '432.gu1', '648.ir1'], 'contains': ['2592.bq1', '2592.dl1', '2592.go1', '3888.dh1', '3888.dy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39916807, 294706904115, 40323593520, 6227827200], 'label': '46656.ir.1296.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iu1', 'old_label': '1296.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714018
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gw1', '432.gx1', '432.gy1', '648.ct1', '648.em1', '648.io1'], 'contains': ['2592.bm1', '2592.dp1', '2592.eh1', '3888.di1', '3888.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 39366316080, 268280812800, 6227827207], 'label': '46656.ir.1296.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714019
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gw1', '432.gz1', '432.ha1', '432.hb1', '648.u1', '648.gs1', '648.im1'], 'contains': ['2592.bk1', '2592.ds1', '2592.em1', '3888.dj1', '3888.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1174327, 39366316080, 6227827207, 435], 'label': '46656.ir.1296.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714020
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.gy1', '432.gz1', '648.v1', '648.en1', '648.in1'], 'contains': ['2592.bn1', '2592.dv1', '2592.er1', '3888.dk1', '3888.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684400, 6227827207], 'label': '46656.ir.1296.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714021
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.gx1', '432.gz1', '432.ha1', '648.w1'], 'contains': ['2592.br1', '2592.ea1', '2592.es1', '3888.dl1', '3888.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684504, 6227827207], 'label': '46656.ir.1296.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '1296.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.gz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714022
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.fe1', '432.hc1', '432.hd1', '432.he1', '648.gq1'], 'contains': ['2592.bl1', '2592.eu1', '2592.ge1', '3888.dm1', '3888.ea1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [93536397441, 6227827200, 104, 41091127], 'label': '46656.ir.1296.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '1296.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ha1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714023
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hc1', '432.hy1', '648.dw1'], 'contains': ['2592.bp1', '2592.ev1', '2592.gk1', '3888.do1', '3888.ea1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [300933848880, 6227827200, 93575951280, 41091127], 'label': '46656.ir.1296.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1296.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714024
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hc1', '432.hd1'], 'contains': ['2592.bt1', '2592.ew1', '2592.gq1', '3888.dr1', '3888.ea1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [295664181445, 6227827200, 643350723578, 41091127], 'label': '46656.ir.1296.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hc1', 'old_label': '1296.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714025
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hf1', '432.hg1', '432.hh1', '432.hi1', '432.hj1', '432.hk1', '432.hl1', '648.u1', '648.gr1', '648.ip1'], 'contains': ['2592.bk1', '2592.ez1', '2592.fr1', '3888.dm1', '3888.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [40323593624, 40323593520, 6227827200, 41091127], 'label': '46656.ir.1296.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714026
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hf1', '432.hm1', '432.ho1', '648.ct1', '648.dx1', '648.iq1'], 'contains': ['2592.bm1', '2592.fe1', '2592.fs1', '3888.dn1', '3888.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 40323593520, 6227827200, 41091127], 'label': '46656.ir.1296.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.he1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714027
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.t1'], 'contains': ['72.bu1', '72.bz1', '72.ce1', '72.fz1', '72.ge1', '72.gr1', '72.hc1', '108.cg1', '108.ch1', '324.be1'], 'core': '46656.a1', 'coset_action_label': '36T16101', 'count': 72, 'diagramx': None, 'generators': [39366316080, 270715783064, 1481684400, 1174645, 1174320, 6267381127, 39957127, 40320], 'label': '46656.ir.36.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '36.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216714028
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hg1', '432.hn1', '432.ho1', '648.v1', '648.dy1', '648.it1'], 'contains': ['2592.bn1', '2592.fh1', '2592.ft1', '3888.dp1', '3888.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 6227827200, 41091127], 'label': '46656.ir.1296.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714029
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hh1', '432.ho1', '432.hp1', '432.hy1', '648.dz1'], 'contains': ['2592.bo1', '2592.fi1', '2592.fu1', '3888.do1', '3888.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [40323593520, 269279866800, 6227827200, 41091127], 'label': '46656.ir.1296.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '1296.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714030
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hf1', '432.hi1', '432.hn1', '432.hp1', '432.hq1', '432.hq2', '648.ir1'], 'contains': ['2592.bq1', '2592.fl1', '2592.fv1', '3888.dq1', '3888.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [355419187635, 40323593520, 6227827200, 41091127], 'label': '46656.ir.1296.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '1296.hh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714031
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hg1', '432.hj1', '432.hm1', '432.hp1', '432.hq1', '432.hq2', '648.w1'], 'contains': ['2592.br1', '2592.fm1', '2592.fw1', '3888.ds1', '3888.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1481684504, 40323593520, 6227827200, 41091127], 'label': '46656.ir.1296.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '1296.hi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714032
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hh1', '432.hk1', '432.hm1', '432.hn1', '432.hp1', '432.hq1', '432.hq2'], 'contains': ['2592.bs1', '2592.fn1', '2592.fx1', '3888.dr1', '3888.eb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [40323593520, 6227827200, 41091127, 270715783395], 'label': '46656.ir.1296.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hj1', 'old_label': '1296.hj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714033
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hr1', '432.hs1', '432.ht1', '432.hu1', '648.x1', '648.gs1', '648.ip1'], 'contains': ['2592.ba1', '2592.bk1', '2592.cj1', '3888.dt1', '3888.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1174320, 6227827200, 435], 'label': '46656.ir.1296.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '1296.hk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714034
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.fm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hr1', '432.hw1', '648.cu1', '648.em1', '648.iq1'], 'contains': ['2592.bf1', '2592.bm1', '2592.ck1', '3888.du1', '3888.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 6227827200], 'label': '46656.ir.1296.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.hl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714035
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.hr1', '432.hs1', '432.hv1', '648.ir1'], 'contains': ['2592.bi1', '2592.bq1', '2592.cn1', '3888.dv1', '3888.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280813235, 39366316080, 1174320, 6227827200], 'label': '46656.ir.1296.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '1296.hm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714036
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hu1', '432.hv1', '432.hw1', '648.y1', '648.dl1', '648.en1', '648.it1', '648.iu1', '648.iv1', '648.iw1'], 'contains': ['2592.bn1', '2592.co1', '3888.ec1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227827200], 'label': '46656.ir.1296.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1296.hn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714037
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ia1', '432.ib1', '432.ic1', '648.l1', '648.z1', '648.hy1', '648.ix1'], 'contains': ['2592.bw1', '2592.do1', '2592.ep1', '3888.ed1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41091120, 325, 39957127, 104], 'label': '46656.ir.1296.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.ho1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ho1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714038
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.t1', '18.p1'], 'contains': ['72.bv1', '72.ca1', '72.cf1', '72.ga1', '72.gf1', '72.gs1', '72.hd1', '108.cg1', '108.ch1', '108.ci1', '324.bd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 39957127, 269279866800, 40320], 'label': '46656.ir.36.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216714039
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.by1', '432.hz1', '432.id1', '648.gq1'], 'contains': ['2592.bu1', '2592.ed1', '2592.ge1', '3888.ee1', '3888.ef1', '3888.eg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [41091120, 93536397441, 6227827207, 104], 'label': '46656.ir.1296.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '1296.hp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714040
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.bz1', '432.hz1', '432.ie1'], 'contains': ['2592.bv1', '2592.ee1', '2592.gf1', '3888.ee1', '3888.eg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [41091120, 174564513075, 6227827207, 104], 'label': '46656.ir.1296.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hq1', 'old_label': '1296.hq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hq1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714041
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.hz1', '432.if1', '432.ig1', '432.ih1', '432.ii1', '648.ba1', '648.gz1', '648.hy1'], 'contains': ['2592.bw1', '2592.ef1', '2592.gg1', '3888.ee1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 325, 6227827207, 104], 'label': '46656.ir.1296.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.hr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hr1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714042
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ia1', '432.ij1', '432.il1', '648.i1', '648.bd1', '648.cy1'], 'contains': ['2592.bx1', '2592.dg1', '2592.el1', '3888.ed1', '3888.eh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 39957127, 37885034880, 31658054835], 'label': '46656.ir.1296.hs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '1296.hs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hs1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714043
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ht1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ib1', '432.ij1', '432.ik1', '648.j1', '648.hz1', '648.im1'], 'contains': ['2592.bz1', '2592.dh1', '2592.em1', '3888.ed1', '3888.ei1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 387037284480, 39957127, 435], 'label': '46656.ir.1296.ht1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.ht1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ht1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714044
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ic1', '432.ik1', '432.il1', '648.bd1', '648.co1', '648.ia1'], 'contains': ['2592.bx1', '2592.dm1', '2592.eg1', '3888.ed1', '3888.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 1481684835, 1481684400, 39957127], 'label': '46656.ir.1296.hu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.hu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714045
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.if1', '432.im1', '432.in1', '648.cz1', '648.gm1', '648.ia1'], 'contains': ['2592.bx1', '2592.dq1', '2592.fy1', '3888.ee1', '3888.ek1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 355419187635, 268280812800, 6227827207], 'label': '46656.ir.1296.hv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '1296.hv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714046
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.id1', '432.ie1', '432.ig1', '432.im1', '432.ip1', '648.gn1'], 'contains': ['2592.by1', '2592.dr1', '2592.fz1', '3888.ee1', '3888.el1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [41091120, 387999647280, 6227827207, 387999647384], 'label': '46656.ir.1296.hw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gn1', 'old_label': '1296.hw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714047
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ih1', '432.im1', '432.io1', '648.be1', '648.go1', '648.im1'], 'contains': ['2592.bz1', '2592.ds1', '2592.ga1', '3888.ee1', '3888.em1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 39366316080, 6227827207, 104], 'label': '46656.ir.1296.hx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.hx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714048
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.id1', '432.iq1', '648.dw1'], 'contains': ['2592.ca1', '2592.dy1', '2592.gk1', '3888.ef1', '3888.el1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 300933848880, 6227827207, 93575951280], 'label': '46656.ir.1296.hy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1296.hy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714049
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '18.j1'], 'contains': ['72.bw1', '72.cb1', '72.cg1', '72.gb1', '72.gg1', '72.gu1', '72.he1', '108.cg1', '324.bf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 39957127, 40320], 'label': '46656.ir.36.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714050
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.hz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.id1', '432.ie1', '432.ir1'], 'contains': ['2592.cb1', '2592.dz1', '2592.gl1', '3888.eg1', '3888.el1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [41091120, 300933848880, 6227827207, 457175462064], 'label': '46656.ir.1296.hz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hz1', 'old_label': '1296.hz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.hz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714051
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ia1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ii1', '432.in1', '432.io1', '432.ip1', '648.be1', '648.gr1', '648.hz1'], 'contains': ['2592.bz1', '2592.eb1', '2592.fr1', '3888.ee1', '3888.en1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 40323593955, 40323593520, 6227827207], 'label': '46656.ir.1296.ia1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.ia1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ia1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714052
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ib1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ij1', '432.is1', '648.b1', '648.dc1', '648.in1', '648.iy1'], 'contains': ['2592.cd1', '2592.df1', '2592.er1', '3888.eh1', '3888.ei1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41091120, 268280812800, 39957127, 37885034880], 'label': '46656.ir.1296.ib1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.ib1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ib1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714053
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ic1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ik1', '432.is1', '648.cd1', '648.ib1', '648.io1'], 'contains': ['2592.cc1', '2592.di1', '2592.eh1', '3888.ei1', '3888.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 301891126320, 1481684400, 39957127], 'label': '46656.ir.1296.ic1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.ic1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ic1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714054
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.id1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.il1', '432.is1', '648.bf1', '648.ce1', '648.dc1'], 'contains': ['2592.cd1', '2592.dk1', '2592.ek1', '3888.eh1', '3888.ej1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 39957127], 'label': '46656.ir.1296.id1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.id1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.id1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714055
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ie1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.im1', '432.it1', '648.dd1', '648.dr1', '648.io1'], 'contains': ['2592.cc1', '2592.dp1', '2592.gh1', '3888.ek1', '3888.el1', '3888.em1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 6227827207], 'label': '46656.ir.1296.ie1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.ie1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ie1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714056
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.if1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.in1', '432.it1', '648.dd1', '648.dx1', '648.ib1'], 'contains': ['2592.cc1', '2592.dt1', '2592.fs1', '3888.ek1', '3888.en1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 268280812800, 40323593520, 6227827207], 'label': '46656.ir.1296.if1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.if1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.if1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714057
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ig1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.io1', '432.it1', '648.bg1', '648.dy1', '648.in1'], 'contains': ['2592.cd1', '2592.dv1', '2592.ft1', '3888.em1', '3888.en1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 6227827207], 'label': '46656.ir.1296.ig1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.ig1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ig1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714058
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ih1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ip1', '432.iq1', '432.ir1', '432.it1', '648.dz1'], 'contains': ['2592.ce1', '2592.dw1', '2592.fu1', '3888.el1', '3888.en1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.1296.ih1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '1296.ih1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ih1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714059
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ii1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.iu1', '432.je1', '648.t1', '648.br1', '648.hi1', '648.iz1', '648.ja1', '648.jb1', '648.jt1'], 'contains': ['2592.ch1', '2592.cr1', '3888.eo1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174320, 104, 1174645, 6267744000], 'label': '46656.ir.1296.ii1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.ii1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ii1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714060
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '18.j1'], 'contains': ['72.bx1', '72.cb1', '72.cd1', '72.gl1', '72.gn1', '72.gv1', '72.hb1', '108.cj1', '324.bg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 39957127, 40320], 'label': '46656.ir.36.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714061
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ij1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.gl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iu1', '432.jf1', '648.bs1', '648.cs1', '648.gt1', '648.jc1', '648.jd1', '648.je1', '648.kf1'], 'contains': ['2592.cf1', '2592.cs1', '3888.eo1', '3888.ep1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [355419187635, 268280812800, 1174320, 6267744000], 'label': '46656.ir.1296.ij1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1296.ij1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ij1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714062
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ik1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iv1', '432.jm1', '648.bm1', '648.cy1', '648.ic1', '648.jc1', '648.jf1', '648.jg1', '648.kg1'], 'contains': ['2592.cf1', '2592.dg1', '3888.eq1', '3888.eu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 39957120, 1481684400, 1521641624], 'label': '46656.ir.1296.ik1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.ik1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ik1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714063
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.il1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iw1', '432.jg1', '432.ji1', '648.bt1', '648.co1', '648.id1', '648.jd1', '648.jh1', '648.ji1', '648.kg1'], 'contains': ['2592.cf1', '2592.dm1', '2592.ex1', '3888.er1', '3888.es1', '3888.et1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 1134007, 1481684400, 1521641624], 'label': '46656.ir.1296.il1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.il1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.il1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714064
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.im1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iw1', '432.jh1', '432.jj1', '648.bu1', '648.ie1', '648.jj1'], 'contains': ['2592.cg1', '2592.dn1', '2592.fa1', '3888.er1', '3888.et1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39957120, 1134007, 325, 1521641624], 'label': '46656.ir.1296.im1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '1296.im1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.im1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714065
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.in1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.iw1', '432.jk1', '432.jl1', '648.l1', '648.bv1', '648.if1', '648.iz1', '648.jk1', '648.jl1', '648.jy1'], 'contains': ['2592.ch1', '2592.do1', '2592.fd1', '3888.er1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 1134007, 325, 39957224], 'label': '46656.ir.1296.in1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.in1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.in1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714066
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.io1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.iv1', '432.jn1', '648.z1', '648.bn1', '648.ig1', '648.ja1', '648.jm1', '648.jn1', '648.jy1'], 'contains': ['2592.ch1', '2592.do1', '3888.eu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39957120, 325, 39957224], 'label': '46656.ir.1296.io1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.io1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.io1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216714067
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ip1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ix1', '432.jo1', '648.bw1', '648.cz1', '648.gp1', '648.jd1', '648.jf1', '648.jo1', '648.kh1'], 'contains': ['2592.cf1', '2592.dq1', '3888.ev1', '3888.ew1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [268280812800, 1174320, 355419187304, 6227827207], 'label': '46656.ir.1296.ip1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.ip1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ip1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714068
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.iq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ix1', '432.jp1', '648.ba1', '648.bx1', '648.he1', '648.iz1', '648.jm1', '648.jp1', '648.kb1'], 'contains': ['2592.ch1', '2592.ef1', '3888.ew1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174320, 6227827207, 104, 1174645], 'label': '46656.ir.1296.iq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.iq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iq1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216714069
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ir1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iy1', '432.jr1', '648.bt1', '648.cy1', '648.gy1', '648.ih1', '648.je1', '648.jo1', '648.jq1'], 'contains': ['2592.cf1', '2592.el1', '3888.ex1', '3888.ey1', '3888.ez1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41050807, 39957120, 1481684400, 1521641624], 'label': '46656.ir.1296.ir1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.ir1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ir1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216714070
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.is1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iy1', '432.jq1', '648.bu1', '648.ii1', '648.jr1'], 'contains': ['2592.cg1', '2592.en1', '3888.ex1', '3888.ez1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1481684725, 41050807, 39957120, 39957224], 'label': '46656.ir.1296.is1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '1296.is1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.is1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216714071
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.u1', '18.p1'], 'contains': ['72.by1', '72.ca1', '72.cc1', '72.go1', '72.gq1', '72.gt1', '72.ha1', '108.cj1', '108.ck1', '324.bh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 6227827207, 39957127, 269279866800, 40320], 'label': '46656.ir.36.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216714072
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.it1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.iy1', '432.js1', '648.z1', '648.bv1', '648.ht1', '648.ij1', '648.jb1', '648.jp1', '648.js1'], 'contains': ['2592.ch1', '2592.ep1', '3888.ex1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050807, 39957120, 325, 39957224], 'label': '46656.ir.1296.it1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.it1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.it1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216714073
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.iu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iz1', '432.jt1', '648.by1', '648.cz1', '648.gt1', '648.id1', '648.jg1', '648.jq1', '648.ki1'], 'contains': ['2592.cf1', '2592.fy1', '3888.fa1', '3888.fb1', '3888.fc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 355419187635, 268280812800, 1174320], 'label': '46656.ir.1296.iu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.iu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216714074
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.iv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.iz1', '432.ju1', '648.bz1', '648.ie1', '648.jr1'], 'contains': ['2592.cg1', '2592.gb1', '3888.fa1', '3888.fc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 268281987445, 1174320, 355419187304], 'label': '46656.ir.1296.iv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '1296.iv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iv1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216714075
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.iw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.iz1', '432.jv1', '648.ba1', '648.ca1', '648.hi1', '648.if1', '648.jn1', '648.js1', '648.ke1'], 'contains': ['2592.ch1', '2592.gg1', '3888.fa1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 1174320, 104, 1174645], 'label': '46656.ir.1296.iw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.iw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iw1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216714076
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ix1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ja1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gj1', '432.ja1', '648.bo1', '648.da1', '648.gu1', '648.jf1', '648.jh1', '648.jq1', '648.kf1'], 'contains': ['2592.cf1', '3888.fd1', '3888.fh1', '3888.fl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [355419187635, 268280812800, 6227464320, 1174320], 'label': '46656.ir.1296.ix1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1296.ix1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ix1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714077
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.iy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.jd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gk1', '432.jb1', '648.bs1', '648.da1', '648.gv1', '648.il1', '648.jg1', '648.ji1', '648.jo1'], 'contains': ['2592.cf1', '3888.fe1', '3888.fi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267381120, 355419187635, 268280812800, 1174320], 'label': '46656.ir.1296.iy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1296.iy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714078
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.iz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.fh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gl1', '432.jc1', '648.bw1', '648.db1', '648.gu1', '648.ic1', '648.je1', '648.ji1', '648.ki1'], 'contains': ['2592.cf1', '3888.ff1', '3888.fj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 268280812800, 1174320, 6227464327], 'label': '46656.ir.1296.iz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.iz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.iz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714079
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ja1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gm1', '432.jd1', '648.by1', '648.db1', '648.gv1', '648.ih1', '648.jc1', '648.jh1', '648.kh1'], 'contains': ['2592.cf1', '3888.fg1', '3888.fk1', '3888.fm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [355419187635, 6267381127, 268280812800, 1174320], 'label': '46656.ir.1296.ja1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1296.ja1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ja1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216714080
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ja1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gh1', '432.ja1', '648.bp1', '648.jj1', '648.jr1'], 'contains': ['2592.cg1', '3888.fd1', '3888.fl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268281987445, 6227464320, 1174320, 355419187304], 'label': '46656.ir.1296.jb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '1296.jb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714081
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gi1', '432.jd1', '648.bz1', '648.ii1', '648.jj1'], 'contains': ['2592.cg1', '3888.fg1', '3888.fm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267381127, 1174320, 268280812904, 1174645], 'label': '46656.ir.1296.jc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '1296.jc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jc1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 216714082
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '18.j1', '18.k1', '18.l1'], 'contains': ['72.e1', '72.l1', '72.v1', '72.bk1', '72.bq1', '72.br1', '72.bt1', '72.cb1', '72.ch1', '72.fc1', '72.hg1', '108.bv1', '108.cl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050800, 39957120, 39916800, 268280812800, 37885034880, 7, 41051125, 31697930984], 'label': '46656.ir.36.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714083
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gn1', '432.ja1', '648.bb1', '648.bq1', '648.hk1', '648.jk1', '648.jm1', '648.js1', '648.jt1'], 'contains': ['2592.ch1', '3888.fd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6227464320, 1174320, 104, 1174645], 'label': '46656.ir.1296.jd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.jd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jd1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714084
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.je1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.go1', '432.jb1', '648.bb1', '648.br1', '648.hn1', '648.ik1', '648.jl1', '648.jn1', '648.jp1'], 'contains': ['2592.ch1', '3888.fe1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 1174320, 104, 1174645], 'label': '46656.ir.1296.je1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.je1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.je1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714085
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gp1', '432.jc1', '648.bc1', '648.bx1', '648.hk1', '648.ig1', '648.jb1', '648.jl1', '648.ke1'], 'contains': ['2592.ch1', '3888.ff1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174320, 6227464327, 104, 1174645], 'label': '46656.ir.1296.jf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1296.jf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jf1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216714086
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gq1', '432.jd1', '648.bc1', '648.ca1', '648.hn1', '648.ij1', '648.ja1', '648.jk1', '648.kb1'], 'contains': ['2592.ch1', '3888.fg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381127, 1174320, 104, 1174645], 'label': '46656.ir.1296.jg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '1296.jg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jg1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216714087
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.je1', '432.jf1', '432.jy1', '648.x1', '648.gw1', '648.ju1'], 'contains': ['2592.cj1', '2592.cp1', '2592.cu1', '3888.eo1', '3888.fn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1174320, 104, 6267744000], 'label': '46656.ir.1296.jh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '1296.jh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714088
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ji1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ha1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jf1', '432.jz1', '648.cu1', '648.fa1', '648.jw1'], 'contains': ['2592.ck1', '2592.cw1', '2592.dc1', '3888.ep1', '3888.fn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 6267744000], 'label': '46656.ir.1296.ji1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '1296.ji1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ji1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714089
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jh1', '432.ji1', '432.jk1', '432.ka1', '648.i1', '648.dg1', '648.kg1'], 'contains': ['2592.ci1', '2592.dg1', '2592.ex1', '3888.er1', '3888.fo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39957120, 1134007, 31697930984, 37885034880], 'label': '46656.ir.1296.jj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '1296.jj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714090
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jg1', '432.jj1', '432.jl1', '432.ka1', '648.j1', '648.ip1', '648.ju1'], 'contains': ['2592.cj1', '2592.dh1', '2592.ez1', '3888.er1', '3888.fp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39957555, 387037284480, 39957120, 1134007], 'label': '46656.ir.1296.jk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.jk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714091
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jg1', '432.kc1', '648.cd1', '648.iq1', '648.jw1'], 'contains': ['2592.ck1', '2592.di1', '2592.fe1', '3888.es1', '3888.fp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 39957120, 1134007, 1481684400], 'label': '46656.ir.1296.jl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.jl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714092
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jh1', '432.ji1', '432.kb1', '648.dh1'], 'contains': ['2592.cl1', '2592.dj1', '2592.ff1', '3888.et1', '3888.fo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [39957120, 1134007, 37885034880, 1521641624], 'label': '46656.ir.1296.jm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '1296.jm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714093
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '18.j1'], 'contains': ['72.k1', '72.n1', '72.bw1', '72.bx1', '72.ch1', '72.gh1', '72.hf1', '108.cm1', '324.bv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 39916800, 6227827200, 1521641624], 'label': '46656.ir.36.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216714094
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ji1', '432.kc1', '648.ce1', '648.di1', '648.kt1'], 'contains': ['2592.cm1', '2592.dk1', '2592.fh1', '3888.es1', '3888.fo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 39957120, 1134007, 1481684400], 'label': '46656.ir.1296.jn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.jn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714095
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jg1', '432.jj1', '432.kb1', '648.ir1'], 'contains': ['2592.cn1', '2592.dl1', '2592.fl1', '3888.et1', '3888.fp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [387037284480, 39957120, 1134007, 1521641624], 'label': '46656.ir.1296.jo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '1296.jo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714096
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jm1', '432.kd1', '648.dc1', '648.de1', '648.kt1'], 'contains': ['2592.cm1', '2592.df1', '2592.dk1', '3888.eq1', '3888.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 1481684400], 'label': '46656.ir.1296.jp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.jp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714097
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jm1', '432.jn1', '432.ke1', '648.bd1', '648.df1', '648.kg1'], 'contains': ['2592.ci1', '2592.dg1', '2592.dm1', '3888.eu1', '3888.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39957120, 31697930984, 37885034880], 'label': '46656.ir.1296.jq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '1296.jq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714098
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jo1', '432.kf1', '648.dd1', '648.em1', '648.jw1'], 'contains': ['2592.ck1', '2592.dp1', '2592.dt1', '3888.ev1', '3888.fr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 6227827207], 'label': '46656.ir.1296.jr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.jr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714099
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.js1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jo1', '432.jp1', '432.kg1', '648.be1', '648.gs1', '648.ju1'], 'contains': ['2592.cj1', '2592.ds1', '2592.eb1', '3888.ew1', '3888.fr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 1174320, 6227827207, 104], 'label': '46656.ir.1296.js1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.js1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.js1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714100
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jq1', '432.jr1', '432.js1', '432.kh1', '648.bd1', '648.dg1', '648.gy1'], 'contains': ['2592.ci1', '2592.eg1', '2592.el1', '3888.ex1', '3888.fs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41050807, 39957120, 31697930984, 37885034880], 'label': '46656.ir.1296.jt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '1296.jt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714101
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ju1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jq1', '432.jr1', '432.ki1', '648.dh1'], 'contains': ['2592.cl1', '2592.ei1', '2592.eq1', '3888.ez1', '3888.fs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [41050807, 1521641955, 39957120, 37885034880], 'label': '46656.ir.1296.ju1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '1296.ju1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ju1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714102
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jr1', '432.kj1', '648.dc1', '648.di1', '648.fu1'], 'contains': ['2592.cm1', '2592.ek1', '2592.er1', '3888.ey1', '3888.fs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 1481684400], 'label': '46656.ir.1296.jv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1296.jv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714103
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jt1', '432.ju1', '432.jv1', '432.kk1', '648.be1', '648.gw1', '648.ip1'], 'contains': ['2592.cj1', '2592.fr1', '2592.ga1', '3888.fa1', '3888.ft1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 435], 'label': '46656.ir.1296.jw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.jw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714104
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.n1', '12.q1', '12.s1', '12.bg1', '12.bi1', '12.br1', '12.bt1', '18.g1', '54.c1', '54.u1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 7, 39957619, 40320, 269279866800], 'label': '46656.ir.6.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714105
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1', '18.j1'], 'contains': ['72.m1', '72.o1', '72.cd1', '72.cg1', '72.ch1', '72.hh1', '72.hi1', '108.cn1', '324.ca1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 39916800, 6227827207, 1521641624], 'label': '46656.ir.36.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714106
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jt1', '432.km1', '648.dd1', '648.fa1', '648.iq1'], 'contains': ['2592.ck1', '2592.fs1', '2592.gh1', '3888.fb1', '3888.ft1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 1174320], 'label': '46656.ir.1296.jx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.jx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714107
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jt1', '432.ju1', '432.kl1', '648.ir1'], 'contains': ['2592.cn1', '2592.fv1', '2592.go1', '3888.fc1', '3888.ft1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 355419187635, 39366316080, 1174320], 'label': '46656.ir.1296.jy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '1296.jy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714108
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.jz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ce1', '432.jw1', '648.cv1', '648.gx1', '648.is1', '648.jv1', '648.jx1', '648.jz1', '648.kc1'], 'contains': ['3888.fu1', '3888.fv1', '3888.fw1', '5184.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41050800, 41051125, 641394472778, 31697930880], 'label': '46656.ir.1296.jz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '1296.jz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.jz1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216714109
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ka1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cf1', '432.jw1', '648.cw1', '648.ka1', '648.kd1'], 'contains': ['3888.fu1', '3888.fw1', '5184.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [2957880565, 37924992000, 2957880240, 463289990028], 'label': '46656.ir.1296.ka1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bq1', 'old_label': '1296.ka1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ka1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714110
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jw1', '432.jx1', '648.cx1', '648.ht1', '648.ik1', '648.jt1', '648.jy1', '648.kb1', '648.ke1'], 'contains': ['2592.ch1', '3888.fu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224], 'label': '46656.ir.1296.kb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1296.kb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kb1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 216714111
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.jx1', '432.kx1', '648.dj1', '648.gy1', '648.il1', '648.kf1', '648.kg1', '648.kh1', '648.ki1'], 'contains': ['2592.cf1', '2592.ci1', '3888.fu1', '3888.fx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 41050800, 31697930984, 37885034880], 'label': '46656.ir.1296.kc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1296.kc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714112
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jy1', '432.jz1', '648.y1', '648.dm1', '648.fj1', '648.kj1', '648.kk1', '648.kl1', '648.ks1'], 'contains': ['2592.co1', '2592.cy1', '3888.fn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6267744000], 'label': '46656.ir.1296.kd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1296.kd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kd1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714113
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ke1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ka1', '432.kb1', '432.kc1', '648.b1', '648.dn1', '648.it1', '648.kj1', '648.km1', '648.kn1', '648.kt1'], 'contains': ['2592.co1', '2592.df1', '2592.fh1', '3888.fo1', '3888.fp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [268280812800, 39957120, 1134007, 37885034880], 'label': '46656.ir.1296.ke1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.ke1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ke1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714114
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kd1', '432.ke1', '648.bf1', '648.dk1', '648.iu1', '648.kk1', '648.ko1', '648.kp1', '648.kt1'], 'contains': ['2592.co1', '2592.dk1', '3888.fq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 37885034880], 'label': '46656.ir.1296.kf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1296.kf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kf1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714115
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kf1', '432.kg1', '648.bg1', '648.do1', '648.en1', '648.kj1', '648.ko1', '648.kq1', '648.ku1'], 'contains': ['2592.co1', '2592.dv1', '3888.fr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227827207], 'label': '46656.ir.1296.kg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1296.kg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kg1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714116
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1', '18.m1', '18.n1', '18.o1'], 'contains': ['72.a1', '72.cp1', '72.hk1', '108.co1', '144.bj1', '972.bd1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 623823424560, 1481684400, 39957120, 39916800, 7, 269279866800], 'label': '46656.ir.36.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714117
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kh1', '432.ki1', '432.kj1', '648.bf1', '648.dn1', '648.fu1', '648.iv1', '648.kl1', '648.kq1', '648.kr1'], 'contains': ['2592.co1', '2592.ek1', '3888.fs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 37885034880], 'label': '46656.ir.1296.kh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.kh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kh1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714118
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ki1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kk1', '432.kl1', '432.km1', '648.bg1', '648.dp1', '648.fj1', '648.it1', '648.kp1', '648.kr1', '648.kv1'], 'contains': ['2592.co1', '2592.ft1', '3888.ft1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400], 'label': '46656.ir.1296.ki1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.ki1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ki1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714119
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kn1', '432.kr1', '432.kt1', '648.bh1', '648.dl1', '648.fl1', '648.km1', '648.ko1', '648.kr1', '648.ks1'], 'contains': ['2592.co1', '11664.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6227464320, 1174320, 1481684400], 'label': '46656.ir.1296.kj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1296.kj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kj1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714120
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ko1', '432.ku1', '648.bh1', '648.dm1', '648.fo1', '648.iw1', '648.kn1', '648.kp1', '648.kq1'], 'contains': ['2592.co1', '11664.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400], 'label': '46656.ir.1296.kk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1296.kk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kk1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714121
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kp1', '432.kv1', '648.bi1', '648.do1', '648.fl1', '648.iu1', '648.kl1', '648.kn1', '648.kv1'], 'contains': ['2592.co1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227464327], 'label': '46656.ir.1296.kl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1296.kl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kl1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714122
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.km1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kq1', '432.ks1', '432.kw1', '648.bi1', '648.dp1', '648.fo1', '648.iv1', '648.kk1', '648.km1', '648.ku1'], 'contains': ['2592.co1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400], 'label': '46656.ir.1296.km1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '1296.km1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.km1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714123
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1', '432.kx1', '648.dq1', '648.fu1', '648.iw1', '648.ks1', '648.kt1', '648.ku1', '648.kv1'], 'contains': ['2592.cm1', '2592.co1', '3888.fx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 37885034880], 'label': '46656.ir.1296.kn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1296.kn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kn1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714124
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ko1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ky1', '432.lb1', '432.lc1', '648.g1', '648.im1', '648.ju1'], 'contains': ['2592.cp1', '2592.dh1', '2592.ds1', '3888.fy1', '3888.fz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 39366316080, 6227827207, 104], 'label': '46656.ir.1296.ko1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.ko1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ko1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714125
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ky1', '432.ld1', '432.le1', '648.k1', '648.hy1', '648.iz1'], 'contains': ['2592.cr1', '2592.do1', '2592.ef1', '3888.fz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 325, 6227827207, 104], 'label': '46656.ir.1296.kp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '1296.kp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kp1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714126
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kz1', '432.lf1', '432.lh1', '432.li1', '648.q1', '648.gr1', '648.ju1'], 'contains': ['2592.cp1', '2592.eb1', '2592.ez1', '3888.ga1', '3888.gb1', '3888.gc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [40323593955, 40323593520, 6227827207, 41091127], 'label': '46656.ir.1296.kq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.kq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714127
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.v1', '18.p1'], 'contains': ['72.r1', '72.bm1', '72.bs1', '72.ca1', '72.ci1', '72.cy1', '72.hl1', '108.cl1', '108.co1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 7, 1521641955, 269279866800], 'label': '46656.ir.36.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '36.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216714128
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kz1', '432.lg1', '432.lj1', '432.lk1', '648.r1'], 'contains': ['2592.cq1', '2592.ec1', '2592.fc1', '3888.ga1', '3888.gc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593845, 6227827207, 104, 41091127], 'label': '46656.ir.1296.kr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.r1', 'old_label': '1296.kr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kr1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714129
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ks1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kz1', '432.ll1', '432.lm1', '432.ln1', '432.lo1', '648.s1', '648.gz1', '648.iz1'], 'contains': ['2592.cr1', '2592.ef1', '2592.fd1', '3888.ga1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [325, 6227827207, 104, 41091127], 'label': '46656.ir.1296.ks1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.ks1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ks1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714130
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.la1', '432.lp1', '432.ls1', '648.q1', '648.gw1', '648.im1'], 'contains': ['2592.cp1', '2592.em1', '2592.ga1', '3888.gd1', '3888.ge1', '3888.gf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [40323593624, 6267744007, 1174327, 40323593520], 'label': '46656.ir.1296.kt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.kt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714131
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ku1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.la1', '432.lq1', '432.lt1', '648.r1'], 'contains': ['2592.cq1', '2592.eo1', '2592.gd1', '3888.gd1', '3888.gf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 1174327, 40323593845, 104], 'label': '46656.ir.1296.ku1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.r1', 'old_label': '1296.ku1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ku1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714132
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.la1', '432.lr1', '432.lu1', '648.s1', '648.hi1', '648.hy1'], 'contains': ['2592.cr1', '2592.ep1', '2592.gg1', '3888.gd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 1174327, 325, 104], 'label': '46656.ir.1296.kv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '1296.kv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kv1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714133
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lb1', '432.lv1', '648.a1', '648.in1', '648.kj1'], 'contains': ['2592.cy1', '2592.df1', '2592.dv1', '3888.fy1', '3888.gg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 6227827207], 'label': '46656.ir.1296.kw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.kw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714134
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lc1', '432.lv1', '648.cb1', '648.io1', '648.jw1'], 'contains': ['2592.cw1', '2592.di1', '2592.dp1', '3888.fy1', '3888.gh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 6227827207], 'label': '46656.ir.1296.kx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.kx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714135
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ky1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lb1', '432.ld1', '432.lw1', '648.h1', '648.hz1', '648.ju1'], 'contains': ['2592.cu1', '2592.dh1', '2592.eb1', '3888.fz1', '3888.gg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [40323593624, 39916807, 40323593520, 6227827207], 'label': '46656.ir.1296.ky1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '1296.ky1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ky1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714136
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.kz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lc1', '432.le1', '432.lw1', '648.cn1', '648.ia1', '648.jd1'], 'contains': ['2592.cs1', '2592.dm1', '2592.dq1', '3888.fz1', '3888.gh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 355419187635, 268280812800, 6227827207], 'label': '46656.ir.1296.kz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '1296.kz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.kz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714137
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.la1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lf1', '432.lg1', '432.ll1', '432.lx1', '648.cp1', '648.gm1', '648.jd1'], 'contains': ['2592.cs1', '2592.dq1', '2592.ex1', '3888.ga1', '3888.gi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [355419187635, 268280812800, 6227827207, 41091127], 'label': '46656.ir.1296.la1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '1296.la1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.la1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714138
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.w1', '12.x1', '18.p1'], 'contains': ['72.bj1', '72.bo1', '72.bv1', '72.by1', '72.ci1', '72.gi1', '72.hj1', '108.cm1', '108.cp1', '324.cf1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 6227827200, 1521641624], 'label': '46656.ir.36.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '36.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216714139
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.li1', '432.lj1', '432.lm1', '432.lx1', '432.ma1', '648.gn1'], 'contains': ['2592.ct1', '2592.dr1', '2592.ey1', '3888.ga1', '3888.gj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [387999647280, 387999647715, 6227827207, 41091127], 'label': '46656.ir.1296.lb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gn1', 'old_label': '1296.lb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714140
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lh1', '432.lk1', '432.ln1', '432.lx1', '648.u1', '648.go1', '648.ju1'], 'contains': ['2592.cu1', '2592.ds1', '2592.ez1', '3888.ga1', '3888.gk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39366316080, 6227827207, 41091127, 435], 'label': '46656.ir.1296.lc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.lc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714141
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ld1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lf1', '432.lz1', '648.cq1', '648.dx1', '648.jw1'], 'contains': ['2592.cw1', '2592.dt1', '2592.fe1', '3888.gb1', '3888.gi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 40323593520, 6227827207, 41091127], 'label': '46656.ir.1296.ld1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.ld1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ld1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714142
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.le1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lf1', '432.lg1', '432.ly1', '648.cr1'], 'contains': ['2592.cx1', '2592.du1', '2592.fg1', '3888.gc1', '3888.gi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 268280812800, 6227827207, 41091127], 'label': '46656.ir.1296.le1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '1296.le1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.le1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714143
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lh1', '432.lz1', '648.v1', '648.dy1', '648.kj1'], 'contains': ['2592.cy1', '2592.dv1', '2592.fh1', '3888.gb1', '3888.gk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 6227827207, 41091127], 'label': '46656.ir.1296.lf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.lf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714144
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.li1', '432.lz1', '432.mb1', '648.dz1'], 'contains': ['2592.cz1', '2592.dw1', '2592.fi1', '3888.gb1', '3888.gj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [40323593520, 269279866800, 6227827207, 41091127], 'label': '46656.ir.1296.lg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '1296.lg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714145
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.li1', '432.lj1', '432.ly1', '432.mc1'], 'contains': ['2592.da1', '2592.dx1', '2592.fk1', '3888.gc1', '3888.gj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [40323593624, 387999647280, 6227827207, 41091127], 'label': '46656.ir.1296.lh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.lh1', 'old_label': '1296.lh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714146
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.li1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lh1', '432.lk1', '432.ly1', '648.w1'], 'contains': ['2592.db1', '2592.ea1', '2592.fm1', '3888.gc1', '3888.gk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [39366316080, 1481684504, 6227827207, 41091127], 'label': '46656.ir.1296.li1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '1296.li1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.li1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714147
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['324.fh1', '432.lo1', '432.ma1', '648.gq1'], 'contains': ['2592.cv1', '2592.ed1', '2592.eu1', '3888.ga1', '3888.gl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [93536397441, 6227827207, 104, 41091127], 'label': '46656.ir.1296.lj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '1296.lj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714148
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lp1', '432.lq1', '432.lr1', '432.md1', '648.cp1', '648.gt1', '648.ia1'], 'contains': ['2592.cs1', '2592.eg1', '2592.fy1', '3888.gd1', '3888.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 1174327, 268280812800, 355419187304], 'label': '46656.ir.1296.lk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '1296.lk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714149
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.y1', '12.z1', '12.ba1', '18.p1'], 'contains': ['72.bn1', '72.bp1', '72.cc1', '72.cf1', '72.ci1', '72.hm1', '72.hp1', '108.cn1', '108.cq1', '324.cg1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 41050800, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.36.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216714150
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ll1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lp1', '432.mf1', '648.cq1', '648.fa1', '648.io1'], 'contains': ['2592.cw1', '2592.eh1', '2592.gh1', '3888.ge1', '3888.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 1174327, 268280812800, 40323593520], 'label': '46656.ir.1296.ll1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.ll1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ll1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714151
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.lp1', '432.lq1', '432.me1', '648.cr1'], 'contains': ['2592.cx1', '2592.ej1', '2592.gi1', '3888.gf1', '3888.gm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 1174327, 268280812800, 40323593955], 'label': '46656.ir.1296.lm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '1296.lm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714152
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ln1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ls1', '432.lt1', '432.lu1', '432.md1', '648.u1', '648.gw1', '648.hz1'], 'contains': ['2592.cu1', '2592.em1', '2592.fr1', '3888.gd1', '3888.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 104], 'label': '46656.ir.1296.ln1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1296.ln1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ln1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714153
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ls1', '432.mf1', '648.v1', '648.fj1', '648.in1'], 'contains': ['2592.cy1', '2592.er1', '2592.ft1', '3888.ge1', '3888.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 1481684400], 'label': '46656.ir.1296.lo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1296.lo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714154
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ls1', '432.lt1', '432.me1', '648.w1'], 'contains': ['2592.db1', '2592.es1', '2592.fw1', '3888.gf1', '3888.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 1481684504], 'label': '46656.ir.1296.lp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '1296.lp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714155
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lv1', '432.lw1', '648.cc1', '648.ib1', '648.jw1'], 'contains': ['2592.dc1', '2592.di1', '2592.dt1', '3888.gg1', '3888.gh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 268280812800, 40323593520, 6227827207], 'label': '46656.ir.1296.lq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1296.lq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714156
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.lx1', '432.ly1', '432.lz1', '648.ct1', '648.dr1', '648.jw1'], 'contains': ['2592.dc1', '2592.dp1', '2592.fe1', '3888.gi1', '3888.gj1', '3888.gk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827207, 41091127], 'label': '46656.ir.1296.lr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.lr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lr1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714157
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ls1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ma1', '432.mb1', '432.mc1', '648.dw1'], 'contains': ['2592.dd1', '2592.dy1', '2592.ev1', '3888.gj1', '3888.gl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [300933848880, 6227827207, 93575951280, 41091127], 'label': '46656.ir.1296.ls1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1296.ls1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ls1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714158
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.md1', '432.me1', '432.mf1', '648.ct1', '648.fa1', '648.ib1'], 'contains': ['2592.dc1', '2592.eh1', '2592.fs1', '3888.gm1', '3888.gn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 268280812800], 'label': '46656.ir.1296.lt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1296.lt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lt1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714159
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hn1', '432.mg1', '648.bj1', '648.hr1', '648.ix1'], 'contains': ['2592.ep1', '11664.bm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174327, 325, 6227752218, 104], 'label': '46656.ir.1296.lu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.o1', 'old_label': '1296.lu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lu1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714160
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.y1', '18.m1'], 'contains': ['72.a1', '72.hn1', '72.hq1', '108.cq1', '144.fj1', '972.bo1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 623823424560, 1481684400, 39957120, 39916800, 6227827207, 269279866800], 'label': '46656.ir.36.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714161
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ho1', '432.mh1', '648.bj1', '648.hs1', '648.ix1'], 'contains': ['2592.ep1', '11664.bn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 6267669018, 325, 104], 'label': '46656.ir.1296.lv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.g1', 'old_label': '1296.lv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lv1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714162
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.hn1', '432.mk1', '648.bk1', '648.fs1', '648.iy1'], 'contains': ['2592.er1', '11664.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174789, 6227752218], 'label': '46656.ir.1296.lw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1', 'old_label': '1296.lw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lw1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714163
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ho1', '432.ml1', '648.bk1', '648.ft1', '648.iy1'], 'contains': ['2592.er1', '11664.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 6267669018, 1481684400, 1174789], 'label': '46656.ir.1296.lx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.c1', 'old_label': '1296.lx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lx1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714164
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.ly1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.hn1', '432.mi1', '648.bl1'], 'contains': ['2592.et2', '11664.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [33138564487, 37885034984, 6227752218, 33139371205], 'label': '46656.ir.1296.ly1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '1296.ly1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.ly1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714165
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1296.lz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.ho1', '432.mj1', '648.bl1'], 'contains': ['2592.et2', '11664.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267669018, 33138564487, 37885034984, 33139371205], 'label': '46656.ir.1296.lz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.bl1', 'old_label': '1296.lz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.lz1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714166
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.e1', '486.a1', '486.f1', '729.a1'], 'contains': ['2916.a1', '2916.b1', '2916.c1', '2916.d1', '2916.g1', '2916.v1', '2916.w1', '2916.x1', '2916.y1', '2916.bc1', '2916.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [499, 443130957804, 444, 40320, 2957880240], 'label': '46656.ir.1458.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714167
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.b1', '162.f1', '486.g1', '729.a1'], 'contains': ['2916.c1', '2916.f1', '2916.h1', '2916.z1', '2916.ba1', '2916.be1', '2916.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [443130957804, 39957619, 444, 40320, 2957880240], 'label': '46656.ir.1458.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714168
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.c1', '162.g1', '486.k1', '729.a1'], 'contains': ['2916.d1', '2916.e1', '2916.h1', '2916.bg1', '2916.bh1', '2916.bi1', '2916.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [499, 444, 443609999724, 40320, 2957880240], 'label': '46656.ir.1458.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714169
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.d1', '162.h1', '486.l1', '729.a1'], 'contains': ['2916.e1', '2916.f1', '2916.g1', '2916.bj1', '2916.bk1', '2916.bm1', '2916.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [444, 443609999724, 40320, 39957619, 2957880240], 'label': '46656.ir.1458.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714170
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.i1', '162.s1', '486.b1', '729.a1'], 'contains': ['2916.k1', '2916.m1', '2916.o1', '2916.x1', '2916.z1', '2916.bg1', '2916.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [499, 443130957804, 444, 39916800, 2957880240], 'label': '46656.ir.1458.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1458.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714171
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.y1', '12.z1'], 'contains': ['72.cj1', '72.ho1', '72.hr1', '108.cq1', '144.fk1', '972.bp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [462923481264, 39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.36.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bv1', 'old_label': '36.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714172
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.j1', '162.t1', '486.c1', '729.a1'], 'contains': ['2916.k1', '2916.n1', '2916.p1', '2916.y1', '2916.ba1', '2916.bi1', '2916.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [443130957804, 444, 39916800, 39957619, 2957880240], 'label': '46656.ir.1458.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714173
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.k1', '162.u1', '486.d1', '729.a1'], 'contains': ['2916.l1', '2916.m1', '2916.p1', '2916.bc1', '2916.be1', '2916.bh1', '2916.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [499, 444, 39916800, 443609999724, 2957880240], 'label': '46656.ir.1458.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714174
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.l1', '162.v1', '486.e1', '729.a1'], 'contains': ['2916.l1', '2916.n1', '2916.o1', '2916.bd1', '2916.bf1', '2916.bl1', '2916.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [444, 39916800, 443609999724, 39957619, 2957880240], 'label': '46656.ir.1458.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714175
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.w1', '486.h1', '486.m1', '486.n1', '729.a1'], 'contains': ['2916.c1', '2916.e1', '2916.i1', '2916.j1', '2916.k1', '2916.l1', '2916.q1', '2916.r1', '2916.s1', '2916.t1', '2916.u1', '2916.bb1', '2916.bo1', '2916.bt1', '2916.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39916800, 6227827207], 'label': '46656.ir.1458.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714176
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.p1', '486.i1', '486.o1', '729.a1'], 'contains': ['2916.d1', '2916.f1', '2916.m1', '2916.n1', '2916.s1', '2916.bp1', '2916.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41050800, 499, 39957564, 39916800], 'label': '46656.ir.1458.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1458.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714177
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.q1', '162.y1', '486.j1', '486.p1', '729.a1'], 'contains': ['2916.g1', '2916.h1', '2916.o1', '2916.p1', '2916.s1', '2916.br1', '2916.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 39957120, 41050800, 39916800, 6227827818], 'label': '46656.ir.1458.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714178
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.z1', '162.bd1', '486.q1', '486.s1', '729.a1'], 'contains': ['2916.x1', '2916.ba1', '2916.bb1', '2916.bh1', '2916.bn1', '2916.bp1', '2916.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 499, 39957564, 443609999724, 2957880240], 'label': '46656.ir.1458.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714179
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.ba1', '162.be1', '486.r1', '486.t1', '729.a1'], 'contains': ['2916.y1', '2916.z1', '2916.bb1', '2916.bl1', '2916.bm1', '2916.bq1', '2916.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39917299, 39957120, 39957564, 443609999724, 2957880240], 'label': '46656.ir.1458.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714180
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.bb1', '162.bf1', '486.u1', '486.w1', '729.a1'], 'contains': ['2916.bc1', '2916.bf1', '2916.bg1', '2916.bk1', '2916.bo1', '2916.bp1', '2916.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 39957257, 39957120, 41050800, 7], 'label': '46656.ir.1458.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714181
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1458.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.bc1', '162.bg1', '486.v1', '486.x1', '729.a1'], 'contains': ['2916.bd1', '2916.be1', '2916.bi1', '2916.bj1', '2916.bo1', '2916.bq1', '2916.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 6227827342, 39957120, 41050800, 7], 'label': '46656.ir.1458.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714182
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1', '9.b1'], 'contains': ['72.ck1', '72.cl1', '72.cm1', '72.cn1', '72.co1', '72.cq1', '72.cr1', '108.cr1', '108.cy1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 39366316080, 2917601004, 499, 24952072764, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.36.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '36.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216714183
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['576.c1', '576.p1', '576.q1', '864.a1', '864.o1', '864.p1', '864.bu1', '864.cs1', '864.di1', '864.dp1', '864.dz1', '864.ez1', '864.ga1', '864.gn1'], 'contains': ['5184.j1', '5184.m1', '5184.n1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 1481684400, 269279866800], 'label': '46656.ir.1728.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1', 'normal_contained_in': ['192.a1', '432.a1', '864.a1'], 'normal_contains': ['46656.a1'], 'normalizer': '1.a1', 'old_label': '1728.a1', 'projective_image': '46656.ir', 'quotient_action_image': '48.48', 'quotient_action_kernel': '36.9', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '1728.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 216714184
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.c1', '576.k1', '864.g1', '864.s1', '864.bb1', '864.bi1', '864.ce1', '864.ck1', '864.cu1', '864.de1', '864.dq1', '864.dx1', '864.ea1', '864.er1', '864.fk1', '864.ge1', '864.gu1'], 'contains': ['5184.b1', '5184.c1', '5184.d1', '5184.j1', '5184.l1', '5184.o1', '5184.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [269279866800, 31658054504, 37885034880], 'label': '46656.ir.1728.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '1728.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714185
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.b1', '576.k1', '864.h1', '864.bc1', '864.cv1', '864.eb1', '864.es1', '864.fl1', '864.gv1'], 'contains': ['5184.b1', '5184.f1', '5184.g1', '5184.l1', '5184.x1', '5184.x2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [31658054504, 37885034880, 269279867125], 'label': '46656.ir.1728.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '1728.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714186
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.b1', '576.l1', '864.b1', '864.i1', '864.cl1', '864.dr1', '864.et1', '864.fa1', '864.fm1'], 'contains': ['5184.b1', '5184.e1', '5184.g1', '5184.k1', '5184.y1', '5184.y2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624, 39366316405, 37885034880], 'label': '46656.ir.1728.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.u1', 'old_label': '1728.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714187
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.b1', '576.c1', '576.l1', '864.c1', '864.j1', '864.t1', '864.bj1', '864.cf1', '864.cm1', '864.cq1', '864.cw1', '864.dn1', '864.ds1', '864.ec1', '864.eu1', '864.fb1', '864.fn1', '864.gf1'], 'contains': ['5184.b1', '5184.d1', '5184.k1', '5184.m1', '5184.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [268280812800, 37885034880, 31658054835], 'label': '46656.ir.1728.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '1728.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.e1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 216714188
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.c1', '576.d1', '576.e1', '576.f1', '576.g1', '576.h1', '576.m1', '864.u1', '864.bk1', '864.cg1', '864.cx1', '864.ed1', '864.fo1', '864.gg1'], 'contains': ['5184.c1', '5184.d1', '5184.n1', '5184.p1', '5184.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [39366316080, 269279866800, 104], 'label': '46656.ir.1728.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '1728.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714189
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.d1', '576.k1', '864.bd1', '864.fp1', '864.gw1'], 'contains': ['5184.c1', '5184.e1', '5184.f1', '5184.g1', '5184.o1', '5184.x1', '5184.x2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1481684725, 2917600664, 301891126320], 'label': '46656.ir.1728.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '1728.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714190
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.i1', '576.j1', '576.m1', '864.cy1', '864.ee1', '864.fq1'], 'contains': ['5184.c1', '5184.g1', '5184.p1', '5184.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [269279866904, 301891126320, 325], 'label': '46656.ir.1728.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.l1', 'old_label': '1728.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714191
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.e1', '576.i1', '576.n1', '864.v1', '864.bl1', '864.bz1', '864.df1', '864.ef1', '864.ff1', '864.gx1'], 'contains': ['5184.c1', '5184.h1', '5184.q1', '5184.r1', '5184.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [387999647280, 93536397441, 387999647384], 'label': '46656.ir.1728.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1', 'old_label': '1728.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714192
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.f1', '576.i1', '576.n1', '864.ca1', '864.eg1', '864.gy1'], 'contains': ['5184.c1', '5184.i1', '5184.r1', '5184.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [387999647280, 325, 463289990028], 'label': '46656.ir.1728.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bp1', 'old_label': '1728.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714193
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1', '18.m1', '18.q1', '18.r1'], 'contains': ['72.b1', '72.cp1', '72.hn1', '108.cx1', '144.bi1', '972.cl1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 623823424560, 1481684400, 39957120, 6227827207, 7, 269279866800], 'label': '46656.ir.36.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714194
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.g1', '576.j1', '576.o1', '864.w1', '864.dg1', '864.gz1'], 'contains': ['5184.c1', '5184.s1', '5184.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [624190336641, 387999647280, 387999647384], 'label': '46656.ir.1728.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.u1', 'old_label': '1728.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.k1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 216714195
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.h1', '576.j1', '576.o1', '864.ha1'], 'contains': ['5184.c1', '5184.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [387999647280, 325, 435907060188], 'label': '46656.ir.1728.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bi1', 'old_label': '1728.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.l1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 216714196
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.b1', '576.d1', '576.k1', '864.be1', '864.bm1', '864.cn1', '864.dt1', '864.fr1', '864.gh1', '864.hb1'], 'contains': ['5184.d1', '5184.e1', '5184.f1', '5184.u1', '5184.x1', '5184.x2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 268280812904, 355419187525], 'label': '46656.ir.1728.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '1728.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714197
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.d1', '576.l1', '864.d1', '864.bn1', '864.cz1', '864.eh1', '864.fc1', '864.fs1', '864.gi1'], 'contains': ['5184.d1', '5184.e1', '5184.g1', '5184.v1', '5184.y1', '5184.y2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684725, 39366316080, 2917600664], 'label': '46656.ir.1728.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '1728.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714198
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.b1', '576.d1', '576.m1', '864.bo1', '864.ft1', '864.gj1'], 'contains': ['5184.d1', '5184.f1', '5184.g1', '5184.w1', '5184.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39366316080, 104, 269279867125], 'label': '46656.ir.1728.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '1728.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714199
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.n1', '864.bp1', '864.fg1', '864.hc1'], 'contains': ['5184.f1', '5184.h1', '5184.i1', '5184.ba1', '5184.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [300933848984, 325, 461482882830], 'label': '46656.ir.1728.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.eg1', 'old_label': '1728.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714200
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.k1', '576.l1', '864.e1', '864.k1', '864.x1', '864.bf1', '864.cb1', '864.cj1', '864.co1', '864.da1', '864.du1', '864.dw1', '864.ei1', '864.ev1', '864.fd1', '864.fu1', '864.hd1'], 'contains': ['5184.a1', '5184.b1', '5184.e1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [325, 31658054504, 37885034880], 'label': '46656.ir.1728.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1728.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.q1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714201
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.k1', '576.m1', '576.n1', '576.o1', '864.y1', '864.bg1', '864.cc1', '864.db1', '864.ej1', '864.fv1', '864.he1'], 'contains': ['5184.a1', '5184.c1', '5184.f1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [301891126320, 325, 104], 'label': '46656.ir.1728.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '1728.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.r1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714202
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.k1', '576.l1', '576.m1', '864.f1', '864.z1', '864.bh1', '864.bq1', '864.cd1', '864.cp1', '864.ct1', '864.dc1', '864.dv1', '864.ek1', '864.ep1', '864.fe1', '864.fw1', '864.gk1', '864.hf1'], 'contains': ['5184.a1', '5184.d1', '5184.g1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 104], 'label': '46656.ir.1728.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '1728.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.s1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714203
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.jw1', '576.n1', '864.ba1', '864.br1', '864.by1', '864.dd1', '864.eq1', '864.fh1', '864.hg1'], 'contains': ['5184.a1', '5184.h1', '5184.i1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [325, 104, 461482882830], 'label': '46656.ir.1728.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '1728.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.t1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714204
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1', '18.m1', '18.s1', '18.t1'], 'contains': ['72.c1', '72.cp1', '72.hq1', '108.dl1', '144.bk1', '972.da1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 7, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.36.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714205
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.c1', '864.l1', '864.bs1', '864.dh1', '864.dy1', '864.ew1', '864.fx1', '864.gl1'], 'contains': ['5184.j1', '5184.k1', '5184.l1', '5184.o1', '5184.p1', '5184.v1', '5184.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684504, 269279866800, 37885034880], 'label': '46656.ir.1728.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '1728.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.u1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714206
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.b1', '864.m1', '864.ex1', '864.fy1'], 'contains': ['5184.k1', '5184.l1', '5184.x1', '5184.y1', '5184.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [270715783064, 37885034880, 269279867125], 'label': '46656.ir.1728.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.j1', 'old_label': '1728.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714207
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.v2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.b1', '864.m2', '864.ex2', '864.fy2'], 'contains': ['5184.k1', '5184.l1', '5184.x2', '5184.y2', '5184.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [355419187304, 37885034880, 269279867125], 'label': '46656.ir.1728.v2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.q1', 'old_label': '1728.v2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.v2', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 216714208
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.b1', '576.c1', '864.n1', '864.bt1', '864.cr1', '864.do1', '864.ey1', '864.fz1', '864.gm1'], 'contains': ['5184.k1', '5184.l1', '5184.m1', '5184.u1', '5184.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1481684835, 268280812800, 37885034880], 'label': '46656.ir.1728.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '1728.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.w1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 216714209
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.c1', '576.d1', '576.r1', '576.s1', '576.t1', '576.t2', '864.bv1', '864.gb1', '864.go1'], 'contains': ['5184.n1', '5184.o1', '5184.u1', '5184.v1', '5184.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [39366316080, 1481684504, 269279866800], 'label': '46656.ir.1728.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '1728.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714210
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ez1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.e1', '576.p1', '576.r1', '864.q1', '864.bx1', '864.ch1', '864.dj1', '864.el1', '864.fi1', '864.gp1'], 'contains': ['5184.n1', '5184.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 655477406640, 269279866800], 'label': '46656.ir.1728.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '1728.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.y1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714211
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.e1', '576.f1', '576.q1', '576.s1', '576.t1', '576.t2', '864.ci1', '864.em1', '864.gq1'], 'contains': ['5184.n1', '5184.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [40323593520, 269279866800, 463289990028], 'label': '46656.ir.1728.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1', 'old_label': '1728.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.z1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714212
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ez1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.g1', '576.p1', '576.s1', '864.r1', '864.dk1', '864.gr1'], 'contains': ['5184.n1', '5184.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [39366316080, 269279866800, 623823424560], 'label': '46656.ir.1728.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '1728.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.ba1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216714213
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.g1', '576.h1', '576.q1', '576.r1', '576.s1', '576.t1', '576.t2', '864.gs1'], 'contains': ['5184.n1', '5184.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [193724576988, 40323593520, 269279866800], 'label': '46656.ir.1728.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.g1', 'old_label': '1728.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bb1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 216714214
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.d1', '864.gc1'], 'contains': ['5184.o1', '5184.p1', '5184.x1', '5184.x2', '5184.y1', '5184.y2', '5184.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [1481684725, 301891126320, 268280812904], 'label': '46656.ir.1728.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.c1', 'old_label': '1728.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714215
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.o1', '12.p1', '12.s1', '12.bl1', '12.bn1', '12.bq1', '12.bv1', '18.h1', '54.d1', '54.v1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6267381127, 499, 7, 40320, 269279866800], 'label': '46656.ir.6.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714216
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '18.n1', '18.q1', '18.s1'], 'contains': ['72.cp1', '108.dm1', '144.bl1', '972.db1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 623823424560, 1481684400, 39957120, 499, 2957558124, 269279866800], 'label': '46656.ir.36.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714217
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.e1', '576.i1', '864.dl1', '864.en1', '864.fj1'], 'contains': ['5184.p1', '5184.q1', '5184.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39366316405, 537124135418, 388956924720], 'label': '46656.ir.1728.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.ci1', 'old_label': '1728.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714218
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.f1', '576.i1', '864.eo1'], 'contains': ['5184.p1', '5184.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [387999647280, 463289990028, 269279867125], 'label': '46656.ir.1728.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.x1', 'old_label': '1728.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.be1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714219
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.g1', '576.j1', '864.dm1'], 'contains': ['5184.p1', '5184.s1', '5184.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [40323593624, 624190336641, 387999647280], 'label': '46656.ir.1728.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.r1', 'old_label': '1728.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bf1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 216714220
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.h1', '576.j1'], 'contains': ['5184.p1', '5184.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 384, 'diagramx': None, 'generators': [269279866904, 461333739315, 301891126320], 'label': '46656.ir.1728.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.g1', 'old_label': '1728.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bg1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 216714221
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.b1', '576.d1', '864.bw1', '864.gd1', '864.gt1'], 'contains': ['5184.u1', '5184.v1', '5184.w1', '5184.x1', '5184.x2', '5184.y2', '5184.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39366316080, 355419187304, 269279867125], 'label': '46656.ir.1728.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '1728.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714222
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1728.bh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['576.a1', '576.b1', '576.d1', '864.bw2', '864.gd2', '864.gt2'], 'contains': ['5184.u1', '5184.v1', '5184.w1', '5184.x1', '5184.x2', '5184.y1', '5184.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [39366316080, 270715783064, 269279867125], 'label': '46656.ir.1728.bh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '1728.bh2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.bh2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714223
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.g1', '648.cb1', '972.a1', '972.b1', '972.e1'], 'contains': ['3888.b1', '3888.e1', '3888.o1', '3888.bj1', '3888.bt1', '3888.de1', '3888.fy1', '5832.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39366316080, 7, 39916800, 6227827207], 'label': '46656.ir.1944.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714224
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.h1', '648.cc1', '972.c1', '972.d1', '972.e1'], 'contains': ['3888.b1', '3888.g1', '3888.q1', '3888.bk1', '3888.bw1', '3888.dy1', '3888.gg1', '5832.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [7, 39916800, 40323593520, 6227827207], 'label': '46656.ir.1944.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1944.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714225
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1', '648.i1', '648.ce1', '972.f1', '972.g1', '972.bt1'], 'contains': ['3888.a1', '3888.i1', '3888.t1', '3888.bn1', '3888.br1', '3888.eh1', '3888.fo1', '5832.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39957120, 7, 1134000, 37885034880], 'label': '46656.ir.1944.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714226
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1', '648.j1', '648.cd1', '972.e1', '972.h1', '972.i1'], 'contains': ['3888.b1', '3888.j1', '3888.u1', '3888.bp1', '3888.bs1', '3888.ei1', '3888.fp1', '5832.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [387037284480, 39957120, 7, 1134000], 'label': '46656.ir.1944.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714227
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '18.n1', '18.r1', '18.t1'], 'contains': ['72.cp1', '108.dn1', '144.bn1', '972.dc1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39917299, 39366316080, 39957120, 41050800, 2957558124, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.36.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714228
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1', '648.c1', '648.cj1', '972.f1', '972.p1', '972.br1'], 'contains': ['3888.a1', '3888.by1', '3888.bz1', '5832.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 499, 39916800, 37885034880], 'label': '46656.ir.1944.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714229
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1', '648.d1', '648.ck1', '972.g1', '972.p1', '972.bs1'], 'contains': ['3888.a1', '3888.bz1', '3888.cd1', '5832.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1481684400, 40320, 39957619, 1481684844], 'label': '46656.ir.1944.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714230
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1', '648.d1', '648.cl1', '972.g1', '972.q1', '972.br1'], 'contains': ['3888.a1', '3888.ca1', '3888.ce1', '5832.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 355419187644, 40320, 39957619], 'label': '46656.ir.1944.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714231
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.k1', '648.f1', '648.cm1', '972.f1', '972.q1', '972.bs1'], 'contains': ['3888.a1', '3888.cc1', '3888.ce1', '5832.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [31658054844, 1134000, 39957619, 37885034880], 'label': '46656.ir.1944.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714232
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.l1', '648.c1', '648.cf1', '972.a1', '972.c1', '972.h1'], 'contains': ['3888.b1', '3888.ck1', '3888.cl1', '5832.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 499, 444, 39916800], 'label': '46656.ir.1944.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1944.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714233
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.m1', '648.e1', '648.cg1', '972.a1', '972.d1', '972.i1'], 'contains': ['3888.b1', '3888.cm1', '3888.cq1', '5832.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [469, 39366316080, 39916800, 6227827818], 'label': '46656.ir.1944.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714234
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.n1', '648.e1', '648.ch1', '972.b1', '972.c1', '972.i1'], 'contains': ['3888.b1', '3888.cn1', '3888.cr1', '5832.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39916800, 6227827818, 40323593520], 'label': '46656.ir.1944.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1944.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714235
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.o1', '648.f1', '648.ci1', '972.b1', '972.d1', '972.h1'], 'contains': ['3888.b1', '3888.co1', '3888.cp1', '5832.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [387037284480, 444, 1134000, 39957619], 'label': '46656.ir.1944.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714236
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.g1', '648.h1', '648.k1', '648.cn1', '972.j1'], 'contains': ['3888.c1', '3888.d1', '3888.p1', '3888.cw1', '3888.cz1', '3888.df1', '3888.fz1', '5832.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [7, 39916800, 6227827207, 435], 'label': '46656.ir.1944.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '1944.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714237
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.i1', '648.j1', '648.l1', '648.co1', '972.j1', '972.k1', '972.bj1'], 'contains': ['3888.c1', '3888.h1', '3888.s1', '3888.cx1', '3888.cy1', '3888.ed1', '3888.er1', '5832.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39957120, 7, 39957224, 1134000], 'label': '46656.ir.1944.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714238
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '18.o1', '18.q1', '18.t1'], 'contains': ['72.cp1', '108.do1', '144.bm1', '972.dd1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 623823424560, 1481684400, 39957120, 6227827818, 269279866800], 'label': '46656.ir.36.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714239
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.q1', '648.r1', '648.s1', '648.u1', '648.cp1', '972.j1'], 'contains': ['3888.d1', '3888.p1', '3888.s1', '3888.dj1', '3888.dm1', '3888.ga1', '3888.gd1', '5832.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [1174327, 39916800, 6227827207, 104], 'label': '46656.ir.1944.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.j1', 'old_label': '1944.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714240
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.q1', '648.v1', '648.cq1', '972.e1'], 'contains': ['3888.e1', '3888.q1', '3888.u1', '3888.dk1', '3888.dp1', '3888.gb1', '3888.ge1', '5832.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1174327, 39916800, 40323593520, 6227827207], 'label': '46656.ir.1944.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714241
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.q1', '648.r1', '648.w1', '648.cr1'], 'contains': ['3888.f1', '3888.r1', '3888.w1', '3888.dl1', '3888.ds1', '3888.gc1', '3888.gf1', '5832.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [1174327, 39916800, 40323593955, 6227827207], 'label': '46656.ir.1944.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.q1', 'old_label': '1944.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714242
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.t1', '648.x1', '648.cs1', '972.j1', '972.l1', '972.bk1'], 'contains': ['3888.d1', '3888.h1', '3888.da1', '3888.dt1', '3888.eo1', '5832.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1174320, 39916800, 6227827200, 104], 'label': '46656.ir.1944.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '1944.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714243
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.u1', '648.v1', '648.w1', '648.ct1', '972.e1'], 'contains': ['3888.g1', '3888.o1', '3888.u1', '3888.dz1', '3888.eb1', '3888.gk1', '3888.gn1', '5832.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1174327, 39366316080, 39916800, 6227827207], 'label': '46656.ir.1944.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714244
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.x1', '648.y1', '648.cu1', '972.e1'], 'contains': ['3888.e1', '3888.g1', '3888.j1', '3888.dd1', '3888.dx1', '3888.ec1', '3888.fn1', '5832.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174320, 39916800, 6227827200], 'label': '46656.ir.1944.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '1944.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714245
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.z1', '648.bd1', '648.cy1', '972.l1', '972.m1', '972.bj1'], 'contains': ['3888.h1', '3888.l1', '3888.ed1', '3888.eu1', '3888.ex1', '5832.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41050807, 39957120, 39957224, 1134000], 'label': '46656.ir.1944.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.u1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714246
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ba1', '648.be1', '648.cz1', '972.j1', '972.m1', '972.bn1'], 'contains': ['3888.h1', '3888.p1', '3888.ee1', '3888.ew1', '3888.fa1', '5832.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [1174320, 39916800, 6227827207, 435], 'label': '46656.ir.1944.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714247
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.z1', '648.bb1', '648.da1', '972.k1', '972.m1', '972.bk1'], 'contains': ['3888.h1', '3888.fd1', '3888.fe1', '5832.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381120, 1174320, 39916800, 104], 'label': '46656.ir.1944.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '1944.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714248
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ba1', '648.bc1', '648.db1', '972.k1', '972.l1', '972.bn1'], 'contains': ['3888.h1', '3888.ff1', '3888.fg1', '5832.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 1174320, 39916800, 435], 'label': '46656.ir.1944.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714249
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1', '18.o1', '18.r1', '18.s1'], 'contains': ['72.cp1', '108.dp1', '144.bo1', '972.de1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 623823424560, 1481684400, 39957120, 6267744618, 269279866800], 'label': '46656.ir.36.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714250
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bd1', '648.bf1', '648.dc1', '972.bt1'], 'contains': ['3888.i1', '3888.k1', '3888.m1', '3888.eh1', '3888.ej1', '3888.fq1', '3888.fs1', '5832.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41050807, 39957120, 1134000, 37885034880], 'label': '46656.ir.1944.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714251
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.be1', '648.bg1', '648.dd1', '972.e1'], 'contains': ['3888.j1', '3888.o1', '3888.q1', '3888.em1', '3888.en1', '3888.fr1', '3888.ft1', '5832.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39366316080, 1174320, 39916800, 6227827207], 'label': '46656.ir.1944.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714252
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bm1', '648.de1', '972.n1', '972.o1', '972.p1', '972.q1', '972.r1', '972.s1', '972.bt1'], 'contains': ['3888.a1', '3888.k1', '3888.y1', '3888.bq1', '3888.eq1', '5832.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 7, 1481684400, 39916800], 'label': '46656.ir.1944.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714253
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.bm1', '648.bn1', '648.df1', '972.t1', '972.u1', '972.bj1'], 'contains': ['3888.c1', '3888.l1', '3888.x1', '3888.cy1', '3888.eu1', '5832.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 7, 39957224, 39916800], 'label': '46656.ir.1944.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1944.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714254
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dc1', '648.bo1', '648.bp1', '648.bq1', '972.t1', '972.v1', '972.bk1'], 'contains': ['3888.x1', '3888.dt1', '3888.fd1', '5832.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1174320, 6227827200, 40320, 435], 'label': '46656.ir.1944.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '1944.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714255
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.de1', '648.bo1', '972.n1', '972.w1', '972.bu1'], 'contains': ['3888.y1', '3888.du1', '3888.fh1', '5832.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 6227827200, 40320], 'label': '46656.ir.1944.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1944.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714256
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dd1', '648.bo1', '648.bp1', '972.x1'], 'contains': ['3888.z1', '3888.dv1', '3888.fl1', '5832.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268280813235, 1174320, 6227827200, 40320], 'label': '46656.ir.1944.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '1944.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.be1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714257
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.df1', '648.br1', '648.bs1', '972.u1', '972.y1', '972.bk1'], 'contains': ['3888.x1', '3888.eo1', '3888.fe1', '5832.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381120, 1174320, 40320, 435], 'label': '46656.ir.1944.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '1944.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714258
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dg1', '648.bs1', '972.o1', '972.z1', '972.bu1'], 'contains': ['3888.y1', '3888.ep1', '3888.fi1', '5832.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 268280812800, 1174320, 40320], 'label': '46656.ir.1944.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1944.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714259
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.bt1', '648.bu1', '648.bv1', '648.dg1', '972.v1', '972.y1', '972.bj1'], 'contains': ['3888.l1', '3888.s1', '3888.x1', '3888.er1', '3888.ex1', '5832.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41050807, 39957120, 39957224, 39916800], 'label': '46656.ir.1944.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714260
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.bb1', '12.bj1', '18.p1'], 'contains': ['72.ct1', '72.cx1', '72.cy1', '72.gf1', '72.gi1', '72.ha1', '72.hm1', '108.cx1', '108.dq1', '324.ea1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 41050800, 7, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.36.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216714261
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bt1', '648.di1', '972.w1', '972.z1', '972.bt1'], 'contains': ['3888.m1', '3888.t1', '3888.y1', '3888.es1', '3888.ey1', '5832.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41050807, 39957120, 1481684400, 39916800], 'label': '46656.ir.1944.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714262
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.bt1', '648.bu1', '648.dh1', '972.x1'], 'contains': ['3888.n1', '3888.v1', '3888.z1', '3888.et1', '3888.ez1', '5832.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [41050807, 39957120, 39916800, 1521641624], 'label': '46656.ir.1944.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '1944.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714263
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.dk1', '648.bw1', '972.n1', '972.z1', '972.bv1'], 'contains': ['3888.y1', '3888.ev1', '3888.fj1', '5832.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 40320, 6227827207], 'label': '46656.ir.1944.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714264
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dl1', '648.bw1', '648.bx1', '972.t1', '972.y1', '972.bn1'], 'contains': ['3888.x1', '3888.ew1', '3888.ff1', '5832.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1174320, 40320, 6227827207, 435], 'label': '46656.ir.1944.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1944.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714265
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dm1', '648.by1', '648.bz1', '648.ca1', '972.u1', '972.v1', '972.bn1'], 'contains': ['3888.x1', '3888.fa1', '3888.fg1', '5832.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 1174320, 40320, 435], 'label': '46656.ir.1944.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714266
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.do1', '648.by1', '972.o1', '972.w1', '972.bv1'], 'contains': ['3888.y1', '3888.fb1', '3888.fk1', '5832.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 40320], 'label': '46656.ir.1944.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714267
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.dn1', '648.by1', '648.bz1', '972.x1'], 'contains': ['3888.z1', '3888.fc1', '3888.fm1', '5832.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [355419187635, 6267381127, 1174320, 40320], 'label': '46656.ir.1944.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '1944.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714268
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cb1', '648.cc1', '648.cn1', '972.ba1', '972.bb1', '972.bc1'], 'contains': ['3888.ba1', '3888.bb1', '3888.be1', '3888.bh1', '3888.bu1', '3888.dg1', '3888.gh1', '5832.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 7, 39916800, 6227827207], 'label': '46656.ir.1944.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714269
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cd1', '648.ce1', '648.co1', '972.bc1', '972.be1', '972.bf1', '972.bg1', '972.bh1', '972.bi1', '972.bt1'], 'contains': ['3888.ba1', '3888.bc1', '3888.bf1', '3888.bn1', '3888.bq1', '3888.ej1', '3888.es1', '5832.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 7, 1481684400, 1134000], 'label': '46656.ir.1944.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714270
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bt1', '648.cf1', '648.cj1', '972.ba1', '972.be1', '972.br1'], 'contains': ['3888.ba1', '3888.by1', '3888.ca1', '5832.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 355419187644, 499, 39916800], 'label': '46656.ir.1944.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '1944.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714271
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.bc1', '12.bx1', '18.p1'], 'contains': ['72.cv1', '72.cw1', '72.cy1', '72.gq1', '72.hd1', '72.hj1', '72.hp1', '108.dl1', '108.dr1', '324.ed1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 7, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.36.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216714272
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bu1', '648.ck1', '648.cl1', '972.bg1', '972.br1', '972.bs1'], 'contains': ['3888.ba1', '3888.bz1', '3888.ce1', '5832.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 40320, 39957619, 37885034880], 'label': '46656.ir.1944.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714273
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bv1', '648.cg1', '648.ch1', '972.ba1', '972.bb1', '972.bh1'], 'contains': ['3888.ba1', '3888.cb1', '3888.cf1', '5832.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 268280812800, 39916800, 6227827818], 'label': '46656.ir.1944.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714274
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bw1', '648.ci1', '648.cm1', '972.bb1', '972.be1', '972.bs1'], 'contains': ['3888.ba1', '3888.cc1', '3888.cd1', '5832.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [1481684400, 1134000, 39957619, 1481684844], 'label': '46656.ir.1944.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714275
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cp1', '648.cq1', '648.cr1', '648.ct1', '972.bc1'], 'contains': ['3888.bb1', '3888.be1', '3888.bf1', '3888.di1', '3888.dn1', '3888.gi1', '3888.gm1', '5832.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1174327, 268280812800, 39916800, 6227827207], 'label': '46656.ir.1944.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714276
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.eg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cs1', '648.cu1', '972.bc1', '972.bl1', '972.bu1'], 'contains': ['3888.bb1', '3888.bc1', '3888.db1', '3888.du1', '3888.ep1', '5832.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 6227827200], 'label': '46656.ir.1944.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1944.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714277
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.cv1', '648.cw1', '648.cx1', '648.dj1', '972.bj1', '972.bk1', '972.bn1'], 'contains': ['3888.h1', '3888.x1', '3888.fu1', '5832.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 41050800, 39957224, 39916800], 'label': '46656.ir.1944.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '1944.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714278
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '648.cv1', '972.bd1', '972.bm1', '972.bo1'], 'contains': ['3888.fv1', '5832.t1', '7776.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [655477406640, 39916800, 2957880240, 31697930880], 'label': '46656.ir.1944.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1944.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.by1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714279
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.cj1', '648.cv1', '648.cw1', '972.bp1'], 'contains': ['3888.fw1', '5832.t1', '7776.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [37924992000, 39916800, 2957880240, 463289990028], 'label': '46656.ir.1944.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bq1', 'old_label': '1944.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.bz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714280
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cy1', '648.dc1', '972.bl1', '972.bq1', '972.bt1'], 'contains': ['3888.bc1', '3888.bd1', '3888.eh1', '3888.eq1', '3888.ey1', '5832.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41050807, 39957120, 1481684400, 1134000], 'label': '46656.ir.1944.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714281
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.cz1', '648.dd1', '972.bc1', '972.bq1', '972.bv1'], 'contains': ['3888.bc1', '3888.be1', '3888.ek1', '3888.ev1', '3888.fb1', '5832.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 6227827207], 'label': '46656.ir.1944.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714282
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '18.e1'], 'contains': ['72.cz1', '72.da1', '72.dd1', '72.dy1', '72.ea1', '72.fn1', '72.fp1', '108.ds1', '108.du1', '108.dv1', '324.cs1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 41091120, 268280812800, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.36.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714283
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ep1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cp1', '648.da1', '972.bf1', '972.bq1', '972.bu1'], 'contains': ['3888.bc1', '3888.fh1', '3888.fi1', '5832.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 268280812800, 1174320, 39916800], 'label': '46656.ir.1944.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1944.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714284
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cq1', '648.db1', '972.bf1', '972.bl1', '972.bv1'], 'contains': ['3888.bc1', '3888.fj1', '3888.fk1', '5832.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 39916800], 'label': '46656.ir.1944.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714285
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.cr1', '216.cs1', '216.ct1', '972.bi1'], 'contains': ['3888.bf1', '3888.go1', '3888.gp1', '5832.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267669018, 268280812800, 1174789, 39916800], 'label': '46656.ir.1944.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.k1', 'old_label': '1944.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ce1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714286
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.de1', '648.df1', '648.dk1', '972.br1', '972.bs1', '972.bt1'], 'contains': ['3888.a1', '3888.m1', '3888.ba1', '3888.bd1', '3888.bg1', '3888.br1', '3888.fq1', '5832.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39957120, 7, 39916800, 37885034880], 'label': '46656.ir.1944.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714287
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dg1', '648.dh1', '648.di1', '648.dn1', '972.bt1'], 'contains': ['3888.k1', '3888.t1', '3888.bd1', '3888.bf1', '3888.bg1', '3888.fo1', '3888.fs1', '5832.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41050807, 39957120, 39916800, 37885034880], 'label': '46656.ir.1944.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714288
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dj1', '648.dq1', '972.bt1', '972.bu1', '972.bv1'], 'contains': ['3888.i1', '3888.y1', '3888.bc1', '3888.bg1', '3888.fx1', '5832.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 39916800, 37885034880], 'label': '46656.ir.1944.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1944.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ch1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714289
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dr1', '648.dx1', '648.gm1', '972.bc1', '972.bw1', '972.bx1'], 'contains': ['3888.bh1', '3888.bn1', '3888.bu1', '3888.db1', '3888.dn1', '3888.ek1', '3888.gi1', '5832.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 6227827207], 'label': '46656.ir.1944.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714290
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dr1', '648.dw1', '648.dz1', '648.gn1', '972.by1'], 'contains': ['3888.bi1', '3888.bo1', '3888.bv1', '3888.dc1', '3888.do1', '3888.el1', '3888.gj1', '5832.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 387999647280, 7, 6227827207], 'label': '46656.ir.1944.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '1944.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714291
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dr1', '648.dy1', '648.go1', '972.e1', '972.bz1', '972.ca1'], 'contains': ['3888.bj1', '3888.bp1', '3888.bw1', '3888.dd1', '3888.dp1', '3888.em1', '3888.gk1', '5832.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 6227827207], 'label': '46656.ir.1944.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ck1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714292
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fm1', '648.ds1', '648.ea1', '972.ba1', '972.bw1', '972.cb1'], 'contains': ['3888.bh1', '3888.by1', '3888.cb1', '5832.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 499, 443130957804, 37885034880], 'label': '46656.ir.1944.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714293
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '18.e1'], 'contains': ['72.cz1', '72.db1', '72.dc1', '72.dz1', '72.eb1', '72.fo1', '72.fq1', '108.dt1', '108.dw1', '324.ct1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174819, 41091120, 268280812800, 6227827207, 7, 104, 325], 'label': '46656.ir.36.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714294
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fn1', '648.dt1', '648.eb1', '972.ba1', '972.bx1', '972.cd1'], 'contains': ['3888.bh1', '3888.ca1', '3888.cf1', '5832.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 40819, 443130957804, 37885034880], 'label': '46656.ir.1944.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714295
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fo1', '648.du1', '648.ec1', '972.bb1', '972.bx1', '972.cb1'], 'contains': ['3888.bh1', '3888.cb1', '3888.cd1', '5832.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 31658054844, 41051299, 37885034880], 'label': '46656.ir.1944.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714296
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fp1', '648.dv1', '648.ed1', '972.bb1', '972.bw1', '972.cd1'], 'contains': ['3888.bh1', '3888.cc1', '3888.cf1', '5832.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 31658054844, 41091619, 37885034880], 'label': '46656.ir.1944.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.co1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714297
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fq1', '648.ds1', '648.ei1', '648.ek1', '972.by1'], 'contains': ['3888.bi1', '3888.cg1', '3888.ch1', '5832.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [301891126320, 499, 443130957804, 444], 'label': '46656.ir.1944.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cs1', 'old_label': '1944.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714298
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fr1', '648.dv1', '648.ej1', '648.el1', '972.by1'], 'contains': ['3888.bi1', '3888.ci1', '3888.cj1', '5832.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [180790853484, 41091619, 301891126320, 444], 'label': '46656.ir.1944.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '1944.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714299
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fs1', '648.ds1', '648.ee1', '972.a1', '972.bz1', '972.cj1'], 'contains': ['3888.bj1', '3888.ck1', '3888.cm1', '5832.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [499, 443130957804, 270715782960, 270715783404], 'label': '46656.ir.1944.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cr1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714300
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ft1', '648.dt1', '648.ef1', '972.a1', '972.ca1', '972.ck1'], 'contains': ['3888.bj1', '3888.cl1', '3888.cq1', '5832.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [40819, 443130957804, 270715782960, 270715783404], 'label': '46656.ir.1944.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714301
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fu1', '648.du1', '648.eg1', '972.b1', '972.ca1', '972.cj1'], 'contains': ['3888.bj1', '3888.cn1', '3888.cp1', '5832.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [180790853484, 41051299, 270715782960, 270715783404], 'label': '46656.ir.1944.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ct1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714302
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fv1', '648.dv1', '648.eh1', '972.b1', '972.bz1', '972.ck1'], 'contains': ['3888.bj1', '3888.co1', '3888.cr1', '5832.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 41091619, 270715782960, 270715783404], 'label': '46656.ir.1944.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714303
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.em1', '648.gp1', '972.n1', '972.bc1', '972.cb1', '972.cc1', '972.cd1', '972.ce1', '972.cf1'], 'contains': ['3888.bh1', '3888.bq1', '3888.di1', '3888.du1', '3888.ev1', '5832.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227827207], 'label': '46656.ir.1944.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714304
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1'], 'contains': ['72.de1', '72.ds1', '72.dt1', '72.dw1', '72.dx1', '72.fr1', '72.fs1', '108.du1', '108.ec1', '324.cu1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [382729979624, 41091120, 457175461950, 6227827207, 300933848880, 499, 7, 325], 'label': '46656.ir.36.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '36.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714305
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['486.h1', '648.dw1', '648.gq1', '972.cg1'], 'contains': ['3888.bl1', '3888.bm1', '3888.bx1', '3888.dw1', '3888.ea1', '3888.ef1', '3888.gl1', '5832.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 7, 6227827207, 93575951280], 'label': '46656.ir.1944.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '1944.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714306
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dx1', '648.dy1', '648.dz1', '648.gr1', '972.e1', '972.ch1', '972.ci1'], 'contains': ['3888.bk1', '3888.bp1', '3888.bt1', '3888.dx1', '3888.eb1', '3888.en1', '3888.gb1', '5832.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 7, 40323593520, 6227827207], 'label': '46656.ir.1944.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714307
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.fz1', '648.ea1', '648.ee1', '648.ei1', '972.c1', '972.ch1', '972.cj1'], 'contains': ['3888.bk1', '3888.ck1', '3888.cn1', '5832.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [499, 443130957804, 444, 269279866800], 'label': '46656.ir.1944.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '1944.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714308
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ga1', '648.eb1', '648.ef1', '972.c1', '972.ci1', '972.ck1'], 'contains': ['3888.bk1', '3888.cl1', '3888.cr1', '5832.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [40819, 443130957804, 444, 269279866800], 'label': '46656.ir.1944.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1944.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.cz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714309
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gb1', '648.ec1', '648.eg1', '972.d1', '972.ci1', '972.cj1'], 'contains': ['3888.bk1', '3888.cm1', '3888.cp1', '5832.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41051299, 443130957804, 444, 269279866800], 'label': '46656.ir.1944.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.da1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714310
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gc1', '648.ed1', '648.eh1', '648.ej1', '972.d1', '972.ch1', '972.ck1'], 'contains': ['3888.bk1', '3888.co1', '3888.cq1', '5832.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091619, 443130957804, 444, 269279866800], 'label': '46656.ir.1944.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.db1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714313
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.em1', '648.en1', '648.gs1', '972.e1', '972.cj1', '972.ck1'], 'contains': ['3888.bj1', '3888.bk1', '3888.bs1', '3888.dk1', '3888.dz1', '3888.ec1', '3888.fr1', '5832.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 6227827207], 'label': '46656.ir.1944.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.de1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714314
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gg1', '486.i1', '648.eo1', '972.cg1'], 'contains': ['3888.bm1', '3888.cs1', '3888.cu1', '5832.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 499, 93576273840, 444], 'label': '46656.ir.1944.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '1944.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.df1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714315
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '18.e1'], 'contains': ['72.df1', '72.di1', '72.dl1', '72.dy1', '72.eb1', '72.fd1', '72.ff1', '108.ds1', '108.ed1', '324.cv1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091120, 268280812800, 499, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.36.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714316
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gh1', '486.j1', '648.ep1', '972.cg1'], 'contains': ['3888.bm1', '3888.ct1', '3888.cv1', '5832.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 469, 6227827818, 93575951280], 'label': '46656.ir.1944.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '1944.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714317
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gi1', '648.eq1', '648.eu1', '972.f1', '972.be1', '972.bw1'], 'contains': ['3888.bn1', '3888.by1', '3888.cc1', '5832.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 41091120, 499, 37885034880], 'label': '46656.ir.1944.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714318
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gj1', '648.ev1', '648.ew1', '972.f1', '972.g1', '972.bg1'], 'contains': ['3888.bn1', '3888.bz1', '3888.ce1', '5832.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [31658054844, 41091120, 39957619, 37885034880], 'label': '46656.ir.1944.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.di1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714319
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gk1', '648.er1', '648.ew1', '972.g1', '972.be1', '972.bx1'], 'contains': ['3888.bn1', '3888.ca1', '3888.cd1', '5832.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41091120, 1481684400, 39957619, 1481684844], 'label': '46656.ir.1944.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714320
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gl1', '648.es1', '648.et1', '972.bh1', '972.bw1', '972.bx1'], 'contains': ['3888.bn1', '3888.cb1', '3888.cf1', '5832.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 469, 268280812800, 6227827818], 'label': '46656.ir.1944.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714321
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gm1', '648.eo1', '648.eq1', '648.ey1', '972.by1'], 'contains': ['3888.bo1', '3888.cg1', '3888.ci1', '5832.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 301891126320, 499, 444], 'label': '46656.ir.1944.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '1944.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714322
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gn1', '648.ep1', '648.es1', '648.ez1', '972.by1'], 'contains': ['3888.bo1', '3888.ch1', '3888.cj1', '5832.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 469, 387999647280, 6227827818], 'label': '46656.ir.1944.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '1944.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714323
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.go1', '648.eq1', '648.eu1', '648.ey1', '972.h1', '972.bz1', '972.ch1'], 'contains': ['3888.bp1', '3888.ck1', '3888.co1', '5832.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 444], 'label': '46656.ir.1944.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714324
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gp1', '648.er1', '648.ev1', '972.h1', '972.ca1', '972.ci1'], 'contains': ['3888.bp1', '3888.cl1', '3888.cp1', '5832.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 387037284480, 444, 39957619], 'label': '46656.ir.1944.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.do1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714325
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gq1', '648.es1', '648.ex1', '972.i1', '972.bz1', '972.ci1'], 'contains': ['3888.bp1', '3888.cm1', '3888.cr1', '5832.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 469, 39366316080, 6227827818], 'label': '46656.ir.1944.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714326
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['23328.f1', '23328.k1', '23328.c1', '23328.h1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.f1', '4.g1', '6.a1', '8.k1', '18.n1', '54.m1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 499, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.2.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.f1', '4.g1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '46656.ir', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216714327
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['12.o1', '12.q1', '12.r1', '12.bm1', '12.bo1', '12.bu1', '12.bw1', '18.i1', '54.e1', '54.w1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6267381127, 7, 39957619, 40320, 269279866800], 'label': '46656.ir.6.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714328
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '18.e1'], 'contains': ['72.df1', '72.dj1', '72.dk1', '72.dz1', '72.ea1', '72.fe1', '72.fg1', '108.dt1', '108.ee1', '324.cw1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091120, 268280812800, 1174819, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.36.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714329
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gr1', '648.et1', '648.ex1', '648.ez1', '972.i1', '972.ca1', '972.ch1'], 'contains': ['3888.bp1', '3888.cn1', '3888.cq1', '5832.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 469, 6227827818, 40323593520], 'label': '46656.ir.1944.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714330
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fa1', '648.gt1', '972.o1', '972.bc1', '972.cm1', '972.cn1', '972.co1', '972.cp1', '972.df1'], 'contains': ['3888.bq1', '3888.bu1', '3888.ep1', '3888.fb1', '3888.gm1', '5832.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320], 'label': '46656.ir.1944.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714331
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gt1', '648.fb1', '648.ff1', '972.p1', '972.be1', '972.cb1', '972.cm1', '972.cq1', '972.cr1', '972.dg1'], 'contains': ['3888.bq1', '3888.by1', '3888.cd1', '5832.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 499, 1481684400, 1521641964], 'label': '46656.ir.1944.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ds1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714332
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.eg1', '648.gu1', '972.n1', '972.bf1', '972.cq1', '972.cs1', '972.ct1', '972.cu1', '972.df1'], 'contains': ['3888.bq1', '3888.fh1', '3888.fj1', '5832.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327], 'label': '46656.ir.1944.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714333
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gv1', '648.fh1', '972.p1', '972.bg1', '972.cc1', '972.cn1', '972.cs1', '972.cv1', '972.dh1'], 'contains': ['3888.bq1', '3888.bz1', '5832.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39917299, 39957120, 1481684400, 1521641964], 'label': '46656.ir.1944.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.du1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714334
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gw1', '648.fc1', '648.fg1', '972.q1', '972.be1', '972.cd1', '972.co1', '972.ct1', '972.cw1', '972.dh1'], 'contains': ['3888.bq1', '3888.ca1', '3888.cc1', '5832.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 1481684400, 1521641964, 1134499], 'label': '46656.ir.1944.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714335
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ej1', '648.gv1', '972.o1', '972.bf1', '972.cf1', '972.cr1', '972.cv1', '972.cw1', '972.cx1'], 'contains': ['3888.bq1', '3888.fi1', '3888.fk1', '5832.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 7, 1174320], 'label': '46656.ir.1944.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714336
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gy1', '648.fd1', '972.r1', '972.bh1', '972.cb1', '972.co1', '972.cs1', '972.cx1', '972.di1'], 'contains': ['3888.bq1', '3888.cb1', '5832.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 1174320, 6227827818], 'label': '46656.ir.1944.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714337
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.gz1', '648.fi1', '972.q1', '972.bg1', '972.ce1', '972.cp1', '972.cu1', '972.cx1', '972.dg1'], 'contains': ['3888.bq1', '3888.ce1', '5832.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41051299, 1481684400, 1521641964], 'label': '46656.ir.1944.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714338
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ha1', '648.fe1', '972.s1', '972.bh1', '972.cd1', '972.cm1', '972.cu1', '972.cv1', '972.dj1'], 'contains': ['3888.bq1', '3888.cf1', '5832.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 6267744618, 1174320], 'label': '46656.ir.1944.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714339
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '18.a1'], 'contains': ['72.dg1', '72.dm1', '72.dp1', '72.ec1', '72.ef1', '72.fh1', '72.fj1', '108.dv1', '108.ed1', '324.cx1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 6227827207, 499, 7, 325], 'label': '46656.ir.36.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714340
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.en1', '216.hb1', '972.r1', '972.bi1', '972.cc1', '972.cp1', '972.cq1', '972.cw1', '972.dj1'], 'contains': ['3888.bq1', '3888.go1', '5832.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 6227464938, 1174320], 'label': '46656.ir.1944.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ea1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714341
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.eo1', '216.hc1', '972.s1', '972.bi1', '972.ce1', '972.cn1', '972.cr1', '972.ct1', '972.di1'], 'contains': ['3888.bq1', '3888.gp1', '5832.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 268280812800, 1174320, 6267381738], 'label': '46656.ir.1944.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.eb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714342
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fa1', '648.fj1', '648.gw1', '972.e1', '972.cy1', '972.cz1'], 'contains': ['3888.bs1', '3888.bt1', '3888.bw1', '3888.fn1', '3888.ft1', '3888.ge1', '3888.gn1', '5832.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320], 'label': '46656.ir.1944.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ec1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714343
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.he1', '648.ff1', '648.fk1', '972.f1', '972.br1', '972.dg1'], 'contains': ['3888.br1', '3888.by1', '3888.ce1', '5832.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31697931324, 39957120, 499, 37885034880], 'label': '46656.ir.1944.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ed1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714344
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hf1', '648.fg1', '648.fm1', '972.f1', '972.bs1', '972.dh1'], 'contains': ['3888.br1', '3888.bz1', '3888.cc1', '5832.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [31697931324, 39957120, 1134499, 37885034880], 'label': '46656.ir.1944.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ee1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714345
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hg1', '648.fh1', '648.fn1', '972.g1', '972.br1', '972.dh1'], 'contains': ['3888.br1', '3888.bz1', '3888.ca1', '5832.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39917299, 31697931324, 39957120, 37885034880], 'label': '46656.ir.1944.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '1944.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ef1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714346
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hh1', '648.fi1', '648.fq1', '972.g1', '972.bs1', '972.dg1'], 'contains': ['3888.br1', '3888.cd1', '3888.ce1', '5832.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [31697931324, 39957120, 41051299, 37885034880], 'label': '46656.ir.1944.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '1944.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.eg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714347
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hi1', '648.fb1', '648.fk1', '972.h1', '972.cj1', '972.cy1'], 'contains': ['3888.bs1', '3888.ck1', '3888.cp1', '5832.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [387037284480, 39957120, 499, 39957564], 'label': '46656.ir.1944.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.eh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714348
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hj1', '648.fc1', '648.fm1', '972.h1', '972.ck1', '972.cz1'], 'contains': ['3888.bs1', '3888.cl1', '3888.co1', '5832.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [387037284480, 39957120, 39957564, 1134499], 'label': '46656.ir.1944.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ei1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714349
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hk1', '648.fd1', '648.fp1', '972.i1', '972.cj1', '972.cz1'], 'contains': ['3888.bs1', '3888.cm1', '3888.cn1', '5832.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 1174320, 6227827818], 'label': '46656.ir.1944.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ej1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714350
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '18.a1'], 'contains': ['72.dg1', '72.dn1', '72.do1', '72.ed1', '72.ef1', '72.fi1', '72.fk1', '108.dw1', '108.ee1', '324.cy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 1174819, 41091120, 1481684400, 6227827207, 7, 325], 'label': '46656.ir.36.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '36.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714351
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hl1', '648.fe1', '648.fr1', '972.i1', '972.ck1', '972.cy1'], 'contains': ['3888.bs1', '3888.cq1', '3888.cr1', '5832.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [469, 39366316080, 6267744618, 1174320], 'label': '46656.ir.1944.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ek1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714352
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cp1', '648.gx1', '972.bd1', '972.cl1', '972.da1', '972.db1', '972.dc1', '972.dd1', '972.de1'], 'contains': ['3888.fv1', '5832.bo1', '7776.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [7, 655477406640, 268240936320, 269202528000], 'label': '46656.ir.1944.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.el1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714353
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fu1', '648.gy1', '972.bt1', '972.cf1', '972.df1', '972.dg1', '972.dh1', '972.di1', '972.dj1'], 'contains': ['3888.bq1', '3888.br1', '3888.ey1', '3888.fs1', '3888.fx1', '5832.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41050800, 7, 37885034880], 'label': '46656.ir.1944.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.em1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714354
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ho1', '648.fv1', '648.fz1', '648.gd1', '972.a1', '972.ch1', '972.cy1'], 'contains': ['3888.bt1', '3888.ck1', '3888.cq1', '5832.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 137, 7], 'label': '46656.ir.1944.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.en1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714355
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hp1', '648.fw1', '648.ga1', '972.a1', '972.ci1', '972.cz1'], 'contains': ['3888.bt1', '3888.cl1', '3888.cm1', '5832.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 6227827342, 7], 'label': '46656.ir.1944.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.eo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714356
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hq1', '648.fx1', '648.gb1', '648.ge1', '972.b1', '972.ch1', '972.cz1'], 'contains': ['3888.bt1', '3888.cn1', '3888.co1', '5832.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6227388862, 6267744007, 39366316080, 7], 'label': '46656.ir.1944.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ep1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714357
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hr1', '648.fy1', '648.gc1', '972.b1', '972.ci1', '972.cy1'], 'contains': ['3888.bt1', '3888.cp1', '3888.cr1', '5832.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174457, 7], 'label': '46656.ir.1944.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.eq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714358
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hs1', '648.fv1', '648.gf1', '972.ba1', '972.bw1', '972.cm1'], 'contains': ['3888.bu1', '3888.by1', '3888.cf1', '5832.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 355419187337, 268280812800, 7], 'label': '46656.ir.1944.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.er1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714359
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ht1', '648.fw1', '648.gg1', '972.ba1', '972.bx1', '972.co1'], 'contains': ['3888.bu1', '3888.ca1', '3888.cb1', '5832.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 274508640142], 'label': '46656.ir.1944.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '1944.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.es1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714360
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hu1', '648.fx1', '648.gh1', '972.bb1', '972.bw1', '972.co1'], 'contains': ['3888.bu1', '3888.cb1', '3888.cc1', '5832.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 361646576062, 268280812800, 7], 'label': '46656.ir.1944.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.et1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714361
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '12.bk1'], 'contains': ['72.dh1', '72.dq1', '72.dr1', '72.eg1', '72.eh1', '72.fl1', '72.fm1', '108.du1', '108.ed1', '324.cz1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 40323593520, 41091120, 6227827207, 499, 7, 325, 269279866800], 'label': '46656.ir.36.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '36.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714362
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hv1', '648.fy1', '648.gi1', '972.bb1', '972.bx1', '972.cm1'], 'contains': ['3888.bu1', '3888.cd1', '3888.cf1', '5832.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 268281987257], 'label': '46656.ir.1944.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.eu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714363
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hw1', '648.gd1', '648.gf1', '648.gj1', '648.gl1', '972.by1'], 'contains': ['3888.bv1', '3888.cg1', '3888.cj1', '5832.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 137, 301891126320, 7], 'label': '46656.ir.1944.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '1944.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ev1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714364
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hx1', '648.ge1', '648.gh1', '648.gk1', '972.by1'], 'contains': ['3888.bv1', '3888.ch1', '3888.ci1', '5832.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6227388862, 6267744007, 301891126320, 7], 'label': '46656.ir.1944.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '1944.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ew1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714365
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hy1', '648.fz1', '648.gf1', '972.c1', '972.bz1', '972.cy1'], 'contains': ['3888.bw1', '3888.ck1', '3888.cr1', '5832.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 7, 40323593657, 40323593520], 'label': '46656.ir.1944.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1944.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ex1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714366
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.hz1', '648.ga1', '648.gg1', '972.c1', '972.ca1', '972.cz1'], 'contains': ['3888.bw1', '3888.cl1', '3888.cn1', '5832.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 26911185982, 7, 40323593520], 'label': '46656.ir.1944.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '1944.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ey1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714367
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ia1', '648.gb1', '648.gh1', '972.d1', '972.bz1', '972.cz1'], 'contains': ['3888.bw1', '3888.cm1', '3888.co1', '5832.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 7, 40323593520, 24952072462], 'label': '46656.ir.1944.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ez1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714368
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ib1', '648.gc1', '648.gi1', '972.d1', '972.ca1', '972.cy1'], 'contains': ['3888.bw1', '3888.cp1', '3888.cq1', '5832.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 2918003897, 7, 40323593520], 'label': '46656.ir.1944.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fa1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714369
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ic1', '486.u1', '648.gj1', '972.cg1'], 'contains': ['3888.bx1', '3888.cs1', '3888.cv1', '5832.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 137, 7, 655477406640], 'label': '46656.ir.1944.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '1944.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714370
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.id1', '486.v1', '648.gk1', '972.cg1'], 'contains': ['3888.bx1', '3888.ct1', '3888.cu1', '5832.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6227388862, 6267744007, 7, 93576273840], 'label': '46656.ir.1944.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '1944.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714371
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gm1', '648.gn1', '648.go1', '648.gq1', '648.gr1', '648.gz1', '972.j1'], 'contains': ['3888.cw1', '3888.cx1', '3888.cz1', '3888.da1', '3888.dm1', '3888.ee1', '3888.ga1', '5832.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [41091120, 7, 6227827207, 104], 'label': '46656.ir.1944.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.j1', 'old_label': '1944.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714372
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1', '18.e1'], 'contains': ['72.da1', '72.dc1', '72.di1', '72.dk1', '72.du1', '72.ej1', '72.el1', '108.dx1', '108.ef1', '324.da1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 268280812800, 6227827207, 499, 7, 104], 'label': '46656.ir.36.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216714373
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gp1', '648.gs1', '648.he1', '972.j1', '972.t1', '972.dk1'], 'contains': ['3888.cw1', '3888.cy1', '3888.dj1', '3888.dt1', '3888.ew1', '5832.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [7, 1174320, 6227827207, 435], 'label': '46656.ir.1944.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1944.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fe1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714374
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gt1', '648.gw1', '648.hi1', '972.j1', '972.u1', '972.dl1'], 'contains': ['3888.cy1', '3888.cz1', '3888.eo1', '3888.fa1', '3888.gd1', '5832.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 7, 1174320, 435], 'label': '46656.ir.1944.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ff1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714375
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fg1', '648.gu1', '648.hk1', '972.k1', '972.t1', '972.dl1'], 'contains': ['3888.cy1', '3888.fd1', '3888.ff1', '5832.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [7, 1174320, 6227464327, 104], 'label': '46656.ir.1944.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1944.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714376
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.fh1', '648.gv1', '648.hn1', '972.k1', '972.u1', '972.dk1'], 'contains': ['3888.cy1', '3888.fe1', '3888.fg1', '5832.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 7, 1174320, 435], 'label': '46656.ir.1944.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714377
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gx1', '648.gy1', '648.ht1', '972.bj1', '972.dk1', '972.dl1'], 'contains': ['3888.cy1', '3888.ex1', '3888.fu1', '5832.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39957224], 'label': '46656.ir.1944.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '1944.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714378
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.hy1', '648.hz1', '648.ia1', '648.im1', '972.j1'], 'contains': ['3888.da1', '3888.df1', '3888.dj1', '3888.ed1', '3888.ee1', '3888.fz1', '3888.gd1', '5832.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [41091120, 1174327, 6227827207, 435], 'label': '46656.ir.1944.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.j1', 'old_label': '1944.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714379
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hz1', '648.ib1', '648.in1', '972.e1'], 'contains': ['3888.dd1', '3888.de1', '3888.dk1', '3888.ei1', '3888.en1', '3888.gg1', '3888.gn1', '5832.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 1174327, 40323593520, 6227827207], 'label': '46656.ir.1944.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714380
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ia1', '648.ib1', '648.io1', '972.bc1'], 'contains': ['3888.db1', '3888.dg1', '3888.di1', '3888.ej1', '3888.ek1', '3888.gh1', '3888.gm1', '5832.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 1174327, 268280812800, 6227827207], 'label': '46656.ir.1944.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '1944.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714381
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.iw1', '648.ic1', '972.n1', '972.bl1', '972.dn1'], 'contains': ['3888.du1', '3888.eq1', '3888.fj1', '5832.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [40327, 268280812800, 1174320, 6227827200], 'label': '46656.ir.1944.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714382
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.id1', '648.ie1', '648.if1', '648.ip1', '972.j1', '972.v1', '972.dm1'], 'contains': ['3888.df1', '3888.dm1', '3888.dt1', '3888.er1', '3888.fa1', '5832.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39916807, 1174320, 6227827200, 104], 'label': '46656.ir.1944.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714383
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1', '18.e1'], 'contains': ['72.db1', '72.dd1', '72.dj1', '72.dl1', '72.du1', '72.ek1', '72.em1', '108.dz1', '108.eg1', '324.db1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 268280812800, 6227827207, 7, 39917299, 104], 'label': '46656.ir.36.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714384
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.id1', '648.iq1', '972.w1', '972.bc1', '972.dn1'], 'contains': ['3888.dg1', '3888.dn1', '3888.du1', '3888.es1', '3888.fb1', '5832.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 268280812800, 1174320, 6227827200], 'label': '46656.ir.1944.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714385
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.id1', '648.ie1', '648.ir1', '972.x1'], 'contains': ['3888.dh1', '3888.dq1', '3888.dv1', '3888.et1', '3888.fc1', '5832.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [39916807, 355419187635, 1174320, 6227827200], 'label': '46656.ir.1944.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '1944.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714386
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ix1', '648.ic1', '648.ig1', '972.l1', '972.t1', '972.dm1'], 'contains': ['3888.dt1', '3888.eu1', '3888.ff1', '5832.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [40327, 1174320, 6227827200, 104], 'label': '46656.ir.1944.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1944.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714387
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.iy1', '648.ih1', '648.ii1', '648.ij1', '972.l1', '972.v1', '972.dk1'], 'contains': ['3888.dt1', '3888.ex1', '3888.fg1', '5832.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 1174320, 39957127, 435], 'label': '46656.ir.1944.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714388
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ja1', '648.ih1', '972.w1', '972.bl1', '972.cf1'], 'contains': ['3888.du1', '3888.ey1', '3888.fk1', '5832.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 39957127], 'label': '46656.ir.1944.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714389
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.iz1', '648.ih1', '648.ii1', '972.x1'], 'contains': ['3888.dv1', '3888.ez1', '3888.fm1', '5832.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [355419187635, 6267381127, 1174320, 39957127], 'label': '46656.ir.1944.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '1944.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ft1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714390
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jb1', '648.ik1', '648.il1', '648.is1', '972.bk1', '972.dk1', '972.dm1'], 'contains': ['3888.dt1', '3888.fe1', '3888.fu1', '5832.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 41050800, 39957224, 6227827200], 'label': '46656.ir.1944.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '1944.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714391
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jc1', '648.il1', '972.bu1', '972.cf1', '972.dn1'], 'contains': ['3888.du1', '3888.fi1', '3888.fx1', '5832.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 6227827200], 'label': '46656.ir.1944.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1944.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714392
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.im1', '648.in1', '648.io1', '972.e1'], 'contains': ['3888.dx1', '3888.dy1', '3888.dz1', '3888.ei1', '3888.em1', '3888.fy1', '3888.ge1', '5832.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 6227827207], 'label': '46656.ir.1944.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714393
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ip1', '648.iq1', '648.ir1', '648.it1', '972.e1'], 'contains': ['3888.de1', '3888.dp1', '3888.dy1', '3888.eb1', '3888.ec1', '3888.fp1', '3888.ft1', '5832.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 6227827200], 'label': '46656.ir.1944.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714394
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1', '18.a1', '18.f1', '18.u1'], 'contains': ['72.dm1', '72.do1', '72.dv1', '72.es1', '72.ex1', '108.ef1', '324.dc1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 499, 7], 'label': '46656.ir.36.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714395
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '648.is1', '972.bm1', '972.cl1', '972.do1'], 'contains': ['3888.fv1', '5832.bx1', '7776.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [655477406640, 6227827200, 2957880240, 31697930880], 'label': '46656.ir.1944.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1944.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fy1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714396
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.jd1', '216.je1', '972.bi1'], 'contains': ['3888.ej1', '3888.go1', '3888.gp1', '5832.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 6267669018, 268280812800, 1174789], 'label': '46656.ir.1944.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.k1', 'old_label': '1944.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.fz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714397
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.iz1', '648.jd1', '648.ju1', '972.j1', '972.y1', '972.dp1'], 'contains': ['3888.eo1', '3888.er1', '3888.ew1', '3888.fz1', '3888.ga1', '5832.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39916807, 1174320, 6227827207, 435], 'label': '46656.ir.1944.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ga1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714398
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.jz1', '648.ja1', '648.jc1', '972.l1', '972.u1', '972.dp1'], 'contains': ['3888.eo1', '3888.eu1', '3888.fg1', '5832.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [40327, 6267381127, 1174320, 435], 'label': '46656.ir.1944.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714399
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ka1', '648.jb1', '648.je1', '972.l1', '972.y1', '972.dl1'], 'contains': ['3888.eo1', '3888.ex1', '3888.ff1', '5832.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [1174320, 6227464327, 39957127, 435], 'label': '46656.ir.1944.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714400
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kc1', '648.jc1', '972.o1', '972.bl1', '972.dr1'], 'contains': ['3888.ep1', '3888.eq1', '3888.fk1', '5832.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [40327, 6267381127, 268280812800, 1174320], 'label': '46656.ir.1944.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714401
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.jd1', '648.jw1', '972.z1', '972.bc1', '972.dr1'], 'contains': ['3888.ep1', '3888.es1', '3888.ev1', '3888.gh1', '3888.gi1', '5832.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 268280812800, 1174320, 6227827207], 'label': '46656.ir.1944.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ge1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714402
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kd1', '648.je1', '972.z1', '972.bl1', '972.df1'], 'contains': ['3888.ep1', '3888.ey1', '3888.fj1', '5832.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 6227464327, 39957127], 'label': '46656.ir.1944.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714403
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kj1', '648.jf1', '972.n1', '972.bq1', '972.dr1'], 'contains': ['3888.eq1', '3888.ev1', '3888.fh1', '5832.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [40327, 268280812800, 1174320, 6227827207], 'label': '46656.ir.1944.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714404
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kk1', '648.jg1', '972.o1', '972.bq1', '972.dn1'], 'contains': ['3888.eq1', '3888.fb1', '3888.fi1', '5832.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381120, 40327, 268280812800, 1174320], 'label': '46656.ir.1944.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714405
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1', '18.a1', '18.g1', '18.v1'], 'contains': ['72.dn1', '72.dp1', '72.dv1', '72.eu1', '72.ez1', '108.eg1', '324.dd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 7, 39917299], 'label': '46656.ir.36.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714406
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ke1', '648.jh1', '648.jj1', '648.jk1', '972.k1', '972.v1', '972.dp1'], 'contains': ['3888.er1', '3888.fd1', '3888.fg1', '5832.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39916807, 6267381127, 1174320, 435], 'label': '46656.ir.1944.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714407
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kf1', '648.ji1', '648.jl1', '972.k1', '972.y1', '972.dm1'], 'contains': ['3888.er1', '3888.fe1', '3888.ff1', '5832.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39916807, 6267381120, 1174320, 104], 'label': '46656.ir.1944.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714408
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kh1', '648.jh1', '972.w1', '972.bf1', '972.dr1'], 'contains': ['3888.es1', '3888.fh1', '3888.fk1', '5832.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 6267381127, 268280812800, 1174320], 'label': '46656.ir.1944.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714409
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ki1', '648.ji1', '972.z1', '972.bf1', '972.dn1'], 'contains': ['3888.es1', '3888.fi1', '3888.fj1', '5832.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 6267381120, 268280812800, 1174320], 'label': '46656.ir.1944.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714410
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kg1', '648.jh1', '648.jj1', '972.x1'], 'contains': ['3888.et1', '3888.fl1', '3888.fm1', '5832.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [39916807, 355419187635, 6267381127, 1174320], 'label': '46656.ir.1944.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '1944.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714411
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kl1', '648.jf1', '648.jm1', '972.m1', '972.t1', '972.dp1'], 'contains': ['3888.eu1', '3888.ew1', '3888.fd1', '5832.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [40327, 1174320, 6227827207, 435], 'label': '46656.ir.1944.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '1944.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714412
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.km1', '648.jg1', '648.jn1', '972.m1', '972.u1', '972.dm1'], 'contains': ['3888.eu1', '3888.fa1', '3888.fe1', '5832.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381120, 40327, 1174320, 104], 'label': '46656.ir.1944.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.go1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714413
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kn1', '648.jo1', '972.z1', '972.bq1', '972.cf1'], 'contains': ['3888.ev1', '3888.ey1', '3888.fi1', '5832.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 6227827207, 39957127], 'label': '46656.ir.1944.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714414
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ko1', '648.jo1', '648.jp1', '972.m1', '972.y1', '972.dk1'], 'contains': ['3888.ew1', '3888.ex1', '3888.fe1', '5832.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [1174320, 6227827207, 39957127, 435], 'label': '46656.ir.1944.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714415
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kp1', '648.jq1', '648.jr1', '648.js1', '972.m1', '972.v1', '972.dl1'], 'contains': ['3888.ex1', '3888.fa1', '3888.fd1', '5832.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 1174320, 39957127, 104], 'label': '46656.ir.1944.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714416
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '18.b1', '18.f1', '18.v1'], 'contains': ['72.dv1', '72.ev1', '72.fa1', '324.de1', '324.ei1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 40819, 7], 'label': '46656.ir.36.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714417
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kr1', '648.jq1', '972.w1', '972.bq1', '972.df1'], 'contains': ['3888.ey1', '3888.fb1', '3888.fh1', '5832.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 1174320, 39957127], 'label': '46656.ir.1944.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714418
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kq1', '648.jq1', '648.jr1', '972.x1'], 'contains': ['3888.ez1', '3888.fc1', '3888.fl1', '5832.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [6267744007, 1174320, 355419187304, 39957127], 'label': '46656.ir.1944.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '1944.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714419
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ks1', '648.jt1', '648.jv1', '648.kf1', '972.bk1', '972.dl1', '972.dp1'], 'contains': ['3888.eo1', '3888.fd1', '3888.fu1', '5832.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957555, 39957120, 41050800, 6267744000], 'label': '46656.ir.1944.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '1944.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 216714420
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ju1', '648.jw1', '648.kj1', '972.e1'], 'contains': ['3888.fn1', '3888.fp1', '3888.fr1', '3888.fy1', '3888.gb1', '3888.gg1', '3888.gk1', '5832.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 6227827207], 'label': '46656.ir.1944.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1944.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714421
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1', '648.jv1', '972.bm1', '972.da1', '972.dq1'], 'contains': ['3888.fv1', '5832.ci1', '7776.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [655477406640, 2957880240, 6267744000, 31697930880], 'label': '46656.ir.1944.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1944.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714422
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hk1', '648.jx1', '972.bd1', '972.do1', '972.dq1'], 'contains': ['3888.fv1', '5832.cj1', '7776.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 655477406640, 2957880240, 31697930880], 'label': '46656.ir.1944.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714423
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jx1', '648.jy1', '648.kg1', '972.bj1', '972.dm1', '972.dp1'], 'contains': ['3888.er1', '3888.eu1', '3888.fu1', '5832.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 39957224], 'label': '46656.ir.1944.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '1944.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714424
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.ku1', '648.jz1', '648.ka1', '648.kb1', '648.kh1', '972.bn1', '972.dk1', '972.dp1'], 'contains': ['3888.ew1', '3888.fg1', '3888.fu1', '5832.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39957555, 39957120, 41050800, 6227827207], 'label': '46656.ir.1944.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.gz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714425
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hn1', '648.jz1', '972.bo1', '972.cl1', '972.dq1'], 'contains': ['3888.fv1', '5832.ck1', '7776.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [655477406640, 6227827207, 2957880240, 31697930880], 'label': '46656.ir.1944.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.ha1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714426
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ho1', '648.jz1', '648.ka1', '972.bp1'], 'contains': ['3888.fw1', '5832.ck1', '7776.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [722937882588, 268242030000, 268240936320, 6227827207], 'label': '46656.ir.1944.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.bp1', 'old_label': '1944.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.hb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714427
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '18.b1', '18.g1', '18.u1'], 'contains': ['72.dv1', '72.ey1', '72.fb1', '324.df1', '324.ej1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 7, 39957619], 'label': '46656.ir.36.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714428
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.kv1', '648.kc1', '648.kd1', '648.ke1', '648.ki1', '972.bn1', '972.dl1', '972.dm1'], 'contains': ['3888.fa1', '3888.ff1', '3888.fu1', '5832.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 39957224], 'label': '46656.ir.1944.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '1944.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.hc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714429
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.hq1', '648.kc1', '972.bo1', '972.da1', '972.do1'], 'contains': ['3888.fv1', '5832.cl1', '7776.cv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 655477406640, 2957880240, 31697930880], 'label': '46656.ir.1944.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1944.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.hd1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714430
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.hr1', '648.kc1', '648.kd1', '972.bp1'], 'contains': ['3888.fw1', '5832.cl1', '7776.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [6267744007, 456696536064, 2957880240, 31697930880], 'label': '46656.ir.1944.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.bp1', 'old_label': '1944.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.he1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714431
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kw1', '648.kf1', '972.bu1', '972.df1', '972.dr1'], 'contains': ['3888.ep1', '3888.fh1', '3888.fx1', '5832.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 6267744000], 'label': '46656.ir.1944.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '1944.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.hf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714432
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kg1', '648.kt1', '972.bt1', '972.dn1', '972.dr1'], 'contains': ['3888.eq1', '3888.es1', '3888.fo1', '3888.fq1', '3888.fx1', '5832.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 37885034880], 'label': '46656.ir.1944.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.hg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714433
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.ky1', '648.kh1', '972.bv1', '972.cf1', '972.dr1'], 'contains': ['3888.ev1', '3888.fk1', '3888.fx1', '5832.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 6227827207], 'label': '46656.ir.1944.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.hh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.hh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714434
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '1944.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.kz1', '648.ki1', '972.bv1', '972.df1', '972.dn1'], 'contains': ['3888.fb1', '3888.fj1', '3888.fx1', '5832.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 39957120, 41050800], 'label': '46656.ir.1944.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '1944.hi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.hi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 216714435
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['864.x1', '864.y1', '864.z1', '864.ba1', '1296.a1', '1296.e1', '1296.ex1', '1296.ey1', '1296.ez1', '1296.fa1', '1296.fb1', '1296.fc1', '1296.fd1', '1296.fe1', '1296.ff1'], 'contains': ['5184.a1', '7776.k1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 325, 104], 'label': '46656.ir.2592.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2592.a1', 'normal_contained_in': ['96.a1', '1296.a1'], 'normal_contains': ['5184.a1'], 'normalizer': '1.a1', 'old_label': '2592.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714436
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '864.c1', '864.e1', '864.j1', '1296.c1', '1296.m1', '1296.p1', '1296.s1', '1296.bb1', '1296.bk1', '1296.ck1'], 'contains': ['5184.b1', '7776.a1', '7776.b1', '7776.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916800, 31658054504, 37885034880], 'label': '46656.ir.2592.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bn1', 'old_label': '2592.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714437
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.c1', '864.d1', '864.f1', '864.g1', '1296.d1', '1296.f1', '1296.i1', '1296.n1', '1296.v1', '1296.y1', '1296.bc1'], 'contains': ['5184.d1', '7776.a1', '7776.c1', '7776.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 39916800, 435], 'label': '46656.ir.2592.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '2592.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714438
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['12.v1', '12.x1', '12.y1', '12.bb1', '12.bc1', '12.cb1', '12.cd1', '18.m1', '18.p1', '24.z1', '162.n1'], 'core': '36.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 624190336641, 6227827207, 7, 269279866800, 1521641624], 'label': '46656.ir.6.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '6.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216714439
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1', '18.j1', '18.u1', '18.v1'], 'contains': ['72.dv1', '72.ew1', '72.fc1', '72.gg1', '72.gh1', '72.hb1', '72.hh1', '108.dq1', '324.ek1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 7, 41051125, 1521641624], 'label': '46656.ir.36.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714440
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '864.d1', '864.e1', '864.i1', '1296.t1', '1296.bd1', '1296.bl1'], 'contains': ['5184.e1', '7776.a1', '7776.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [325, 1481684504, 39916800], 'label': '46656.ir.2592.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '2592.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714441
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '864.d1', '864.f1', '864.h1', '1296.g1', '1296.z1', '1296.be1'], 'contains': ['5184.g1', '7776.a1', '7776.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316405, 39916800, 104], 'label': '46656.ir.2592.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '2592.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714442
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.e1', '864.f1', '864.k1', '1296.e1', '1296.h1', '1296.l1', '1296.u1', '1296.ba1', '1296.bf1', '1296.bm1'], 'contains': ['5184.a1', '7776.a1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [325, 39916800, 104], 'label': '46656.ir.2592.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '2592.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.f1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714443
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '864.c1', '864.n1', '1296.q1', '1296.bg1', '1296.cl1'], 'contains': ['5184.k1', '7776.b1', '7776.d1', '7776.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684504, 39916800, 37885034880], 'label': '46656.ir.2592.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '2592.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714444
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.c1', '864.o1', '1296.b1', '1296.j1', '1296.o1', '1296.r1', '1296.w1', '1296.bh1', '1296.cm1'], 'contains': ['5184.m1', '7776.b1', '7776.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684400, 39916800], 'label': '46656.ir.2592.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '2592.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.h1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216714445
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.c1', '864.d1', '864.l1', '1296.k1', '1296.x1', '1296.bi1'], 'contains': ['5184.v1', '7776.c1', '7776.d1', '7776.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 1481684835, 39916800], 'label': '46656.ir.2592.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '2592.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714446
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '864.d1', '864.m1', '1296.bj1'], 'contains': ['5184.y1', '7776.d1', '7776.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [39366316405, 1481684504, 39916800], 'label': '46656.ir.2592.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.g1', 'old_label': '2592.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714447
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.b1', '864.d1', '864.m2', '1296.bj2'], 'contains': ['5184.y2', '7776.d1', '7776.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [31658054725, 39916800, 33139370984], 'label': '46656.ir.2592.j2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.p1', 'old_label': '2592.j2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.j2', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714448
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.g1', '864.h1', '864.i1', '864.j1', '864.k1', '1296.bp1', '1296.bq1', '1296.bu1', '1296.by1', '1296.cc1', '1296.cf1', '1296.ck1'], 'contains': ['5184.b1', '7776.a1', '7776.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [268280812800, 39916800, 355419187304], 'label': '46656.ir.2592.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '2592.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714449
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.dm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.g1', '864.l1', '864.o1', '1296.bn1', '1296.br1', '1296.bt1', '1296.bv1', '1296.cb1', '1296.cd1', '1296.cg1'], 'contains': ['5184.j1', '7776.c1', '7776.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 268280812800, 39916800], 'label': '46656.ir.2592.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '2592.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714450
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1', '18.e1'], 'contains': ['72.ei1', '72.ej1', '72.em1', '72.fd1', '72.fg1', '72.fn1', '72.fq1', '108.ei1', '108.eu1', '324.dh1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 6267744007, 1174645, 1174320, 268280812800, 499, 7, 104], 'label': '46656.ir.36.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714451
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.i1', '864.j1', '864.l1', '864.m1', '864.m2', '864.n1', '1296.bz1', '1296.ch1', '1296.cl1'], 'contains': ['5184.k1', '7776.d1', '7776.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [268280812800, 1481684504, 39916800], 'label': '46656.ir.2592.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.u1', 'old_label': '2592.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714452
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.g1', '864.h1', '864.l1', '864.m1', '864.m2', '864.n1', '1296.bs1', '1296.ce1', '1296.ci1'], 'contains': ['5184.l1', '7776.e1', '7776.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624, 268280812800, 39916800], 'label': '46656.ir.2592.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '2592.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714453
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.j1', '864.n1', '864.o1', '1296.bo1', '1296.bw1', '1296.bx1', '1296.ca1', '1296.cj1', '1296.cm1', '1296.cn1'], 'contains': ['5184.m1', '7776.b1', '7776.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 39916800, 37885034880], 'label': '46656.ir.2592.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '2592.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714474
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bb1', '864.bd1', '864.bv1', '1296.gg1'], 'contains': ['5184.o1', '7776.n1', '7776.p1', '7776.q1', '7776.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [382729979955, 387999647280, 6227827200], 'label': '46656.ir.2592.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ds1', 'old_label': '2592.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714454
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.dr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.p1', '864.s1', '1296.bn1', '1296.co1', '1296.cp1', '1296.cu1', '1296.cx1', '1296.da1', '1296.dd1', '1296.dg1', '1296.dh1', '1296.di1', '1296.dj1', '1296.dk1', '1296.dl1', '1296.dm1', '1296.dn1'], 'contains': ['5184.j1', '7776.g1', '7776.h1', '7776.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7, 269279866800, 37885034880], 'label': '46656.ir.2592.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '2592.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714455
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.p1', '864.t1', '1296.b1', '1296.bo1', '1296.cq1', '1296.cv1', '1296.cy1', '1296.cz1', '1296.db1', '1296.do1', '1296.dp1', '1296.dq1', '1296.dr1', '1296.ds1', '1296.dt1', '1296.du1', '1296.dv1'], 'contains': ['5184.m1', '7776.g1', '7776.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 37885034880], 'label': '46656.ir.2592.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '2592.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.q1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216714456
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.cw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.p1', '864.q1', '864.r1', '864.u1', '1296.cr1', '1296.cw1', '1296.dc1', '1296.dw1', '1296.dx1', '1296.dy1', '1296.dz1'], 'contains': ['5184.n1', '7776.h1', '7776.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 7, 269279866800], 'label': '46656.ir.2592.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '2592.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714457
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.q1', '864.v1', '1296.cs1', '1296.ct1', '1296.de1', '1296.ea1', '1296.eb1', '1296.ec1', '1296.ed1'], 'contains': ['5184.q1', '7776.h1', '7776.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [301891126320, 7, 655477406640], 'label': '46656.ir.2592.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '2592.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.s1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714458
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.r1', '864.w1', '1296.df1', '1296.ee1', '1296.ef1'], 'contains': ['5184.s1', '7776.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [301891126320, 7, 623823424560], 'label': '46656.ir.2592.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '2592.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.t1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 216714459
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.de1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.s1', '864.t1', '864.x1', '1296.c1', '1296.bp1', '1296.eg1', '1296.em1', '1296.ep1', '1296.eq1', '1296.et1'], 'contains': ['5184.b1', '7776.g1', '7776.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [7, 37885034880, 31658054835], 'label': '46656.ir.2592.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '2592.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.u1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714460
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.z1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.s1', '864.u1', '864.v1', '864.w1', '864.y1', '1296.eh1', '1296.en1', '1296.eu1'], 'contains': ['5184.c1', '7776.h1', '7776.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [301891126320, 7, 435], 'label': '46656.ir.2592.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '2592.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714461
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1', '18.e1'], 'contains': ['72.ei1', '72.ek1', '72.el1', '72.fe1', '72.ff1', '72.fo1', '72.fp1', '108.ek1', '108.ev1', '324.di1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 1174320, 6227827818, 104, 1174645], 'label': '46656.ir.36.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cv1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216714462
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.s1', '864.t1', '864.u1', '864.z1', '1296.d1', '1296.ei1', '1296.ej1', '1296.eo1', '1296.er1', '1296.es1', '1296.ev1'], 'contains': ['5184.d1', '7776.i1', '7776.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 7, 104], 'label': '46656.ir.2592.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '2592.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.w1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714463
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ca1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.gx1', '864.v1', '864.ba1', '1296.ek1', '1296.el1', '1296.ew1'], 'contains': ['5184.h1', '7776.j1', '7776.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [7, 325, 641394472778], 'label': '46656.ir.2592.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '2592.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714464
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.eo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bb1', '864.bc1', '864.bf1', '864.bi1', '1296.bq1', '1296.eg1', '1296.fh1', '1296.fo1', '1296.fr1', '1296.fx1', '1296.gj1'], 'contains': ['5184.b1', '7776.l1', '7776.m1', '7776.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [355419187635, 268280812800, 6227827200], 'label': '46656.ir.2592.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '2592.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714465
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bb1', '864.bd1', '864.bg1', '864.bk1', '864.bl1', '1296.eh1', '1296.fi1', '1296.fy1'], 'contains': ['5184.c1', '7776.l1', '7776.n1', '7776.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [387999647280, 387999647715, 6227827200], 'label': '46656.ir.2592.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cz1', 'old_label': '2592.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714466
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bb1', '864.be1', '864.bh1', '864.bj1', '1296.f1', '1296.ei1', '1296.fj1', '1296.fl1', '1296.fu1', '1296.fz1', '1296.hk1'], 'contains': ['5184.d1', '7776.l1', '7776.o1', '7776.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 6227827200, 435], 'label': '46656.ir.2592.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '2592.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714467
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.eo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bd1', '864.be1', '864.bf1', '864.bm1', '1296.fp1', '1296.ga1', '1296.gk1'], 'contains': ['5184.e1', '7776.l1', '7776.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280813125, 6227827200, 355419187304], 'label': '46656.ir.2592.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '2592.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714468
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bc1', '864.bd1', '864.be1', '864.bg1', '864.bo1', '864.bp1', '1296.gb1'], 'contains': ['5184.f1', '7776.l1', '7776.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [295664181445, 6227827200, 104], 'label': '46656.ir.2592.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ds1', 'old_label': '2592.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714469
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bc1', '864.bd1', '864.bh1', '864.bn1', '1296.g1', '1296.fv1', '1296.gc1'], 'contains': ['5184.g1', '7776.l1', '7776.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [34096648424, 39366316405, 6227827200], 'label': '46656.ir.2592.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '2592.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714470
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bf1', '864.bg1', '864.bh1', '864.bq1', '864.br1', '1296.h1', '1296.ex1', '1296.fg1', '1296.fq1', '1296.fw1', '1296.gd1', '1296.gl1'], 'contains': ['5184.a1', '7776.l1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [325, 6227827200, 104], 'label': '46656.ir.2592.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '2592.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.be1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714471
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bb1', '864.bu1', '1296.br1', '1296.co1', '1296.fk1', '1296.fm1', '1296.fs1', '1296.ge1', '1296.hl1'], 'contains': ['5184.j1', '7776.m1', '7776.n1', '7776.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827200], 'label': '46656.ir.2592.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '2592.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714472
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1', '18.a1', '18.h1', '18.w1'], 'contains': ['72.er1', '72.es1', '72.ez1', '72.fh1', '72.fk1', '108.eu1', '324.dj1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 1174320, 1174645, 499, 7], 'label': '46656.ir.36.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cw1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714473
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bb1', '864.bc1', '864.bs1', '1296.bs1', '1296.ft1', '1296.gf1'], 'contains': ['5184.l1', '7776.m1', '7776.q1', '7776.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 387999647715, 6227827200], 'label': '46656.ir.2592.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '2592.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714475
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bb1', '864.be1', '864.bt1', '1296.fn1', '1296.gh1', '1296.hm1'], 'contains': ['5184.u1', '7776.o1', '7776.p1', '7776.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 268280812904, 6227827200], 'label': '46656.ir.2592.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '2592.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714476
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bc1', '864.bd1', '864.be1', '864.bw1', '1296.gi1'], 'contains': ['5184.x2', '7776.p1', '7776.q1', '7776.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [295664181445, 39366316184, 6227827200], 'label': '46656.ir.2592.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ds1', 'old_label': '2592.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714477
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['864.bc1', '864.bd1', '864.be1', '864.bw2', '1296.gi2'], 'contains': ['5184.x1', '7776.p1', '7776.q1', '7776.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [39366316405, 6227827200, 355419187304], 'label': '46656.ir.2592.bj2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ds1', 'old_label': '2592.bj2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bj2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714478
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bi1', '864.bj1', '864.bk1', '864.bm1', '864.bn1', '864.bo1', '864.bq1', '1296.i1', '1296.ej1', '1296.gn1', '1296.gt1', '1296.gx1', '1296.hd1', '1296.hk1'], 'contains': ['5184.d1', '7776.l1', '7776.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [40323593624, 40323593520, 6227827200], 'label': '46656.ir.2592.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '2592.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714479
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.cc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.is1', '864.bl1', '864.bp1', '864.br1', '1296.ek1', '1296.gm1', '1296.ha1'], 'contains': ['5184.h1', '7776.l1', '7776.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [623710972161, 6227827200, 104], 'label': '46656.ir.2592.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.de1', 'old_label': '2592.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714480
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.di1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bi1', '864.bs1', '864.bu1', '1296.bt1', '1296.cp1', '1296.gp1', '1296.gu1', '1296.gw1', '1296.he1', '1296.hl1'], 'contains': ['5184.j1', '7776.m1', '7776.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 40323593520, 6227827200], 'label': '46656.ir.2592.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '2592.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714481
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bj1', '864.bt1', '864.bu1', '1296.j1', '1296.cq1', '1296.gq1', '1296.gs1', '1296.gy1', '1296.hf1', '1296.hn1'], 'contains': ['5184.m1', '7776.o1', '7776.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684400, 6227827200], 'label': '46656.ir.2592.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '2592.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714482
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.cp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bk1', '864.bu1', '864.bv1', '864.bx1', '1296.cr1', '1296.gr1', '1296.hg1'], 'contains': ['5184.n1', '7776.n1', '7776.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593520, 269279866800, 6227827200], 'label': '46656.ir.2592.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '2592.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714483
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1', '18.a1', '18.i1', '18.x1'], 'contains': ['72.er1', '72.eu1', '72.ex1', '72.fi1', '72.fj1', '108.ev1', '324.dk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400, 1481684504, 6227827818, 1174645], 'label': '46656.ir.36.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cx1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714484
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ez1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.bl1', '864.bx1', '1296.cs1', '1296.go1', '1296.hb1'], 'contains': ['5184.q1', '7776.n1', '7776.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [624302466480, 300933848880, 6227827200], 'label': '46656.ir.2592.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '2592.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714485
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.u1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bi1', '864.bm1', '864.bt1', '864.bv1', '864.bw1', '864.bw2', '1296.gv1', '1296.hh1', '1296.hm1'], 'contains': ['5184.u1', '7776.p1', '7776.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [355419187635, 40323593520, 6227827200], 'label': '46656.ir.2592.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '2592.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714486
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bj1', '864.bn1', '864.bs1', '864.bv1', '864.bw1', '864.bw2', '1296.k1', '1296.gz1', '1296.hi1'], 'contains': ['5184.v1', '7776.r1', '7776.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684835, 40323593520, 6227827200], 'label': '46656.ir.2592.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '2592.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714487
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bk1', '864.bo1', '864.bs1', '864.bt1', '864.bv1', '864.bw1', '864.bw2', '1296.hj1'], 'contains': ['5184.w1', '7776.q1', '7776.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [270715783064, 40323593520, 6227827200], 'label': '46656.ir.2592.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '2592.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714488
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bl1', '864.bp1', '1296.hc1'], 'contains': ['5184.ba1', '7776.q1', '7776.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [295664181445, 6227827200, 643350723578], 'label': '46656.ir.2592.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.eg1', 'old_label': '2592.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714489
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.cv1', '864.by1', '864.bz1', '1296.el1', '1296.gm1', '1296.hp1'], 'contains': ['5184.h1', '7776.u1', '7776.v1', '7776.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [41091120, 93536397441, 104], 'label': '46656.ir.2592.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fx1', 'old_label': '2592.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714490
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.cw1', '864.by1', '864.ca1', '1296.hq1'], 'contains': ['5184.i1', '7776.u1', '7776.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [41091120, 174564190515, 104], 'label': '46656.ir.2592.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hz1', 'old_label': '2592.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714491
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.by1', '864.cb1', '864.cc1', '864.cd1', '1296.l1', '1296.ey1', '1296.fg1', '1296.ho1', '1296.hr1'], 'contains': ['5184.a1', '7776.u1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 325, 104], 'label': '46656.ir.2592.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '2592.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bw1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714492
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cb1', '864.ce1', '864.cf1', '1296.m1', '1296.bu1', '1296.em1', '1296.fh1', '1296.hs1', '1296.hu1', '1296.hv1'], 'contains': ['5184.b1', '7776.u1', '7776.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 31658054504, 37885034880], 'label': '46656.ir.2592.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '2592.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714493
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.bz1', '864.ca1', '864.cc1', '864.ce1', '864.cg1', '1296.en1', '1296.fi1', '1296.hw1'], 'contains': ['5184.c1', '7776.u1', '7776.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [41091120, 301891126320, 104], 'label': '46656.ir.2592.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.de1', 'old_label': '2592.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.by1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714494
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '18.b1', '18.h1', '18.x1'], 'contains': ['72.er1', '72.ev1', '72.fb1', '324.dl1', '324.en1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400, 1481684504, 6267381738, 1174645], 'label': '46656.ir.36.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cy1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714495
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cd1', '864.ce1', '864.cf1', '864.cg1', '1296.n1', '1296.eo1', '1296.fj1', '1296.gn1', '1296.ht1', '1296.hx1', '1296.ia1'], 'contains': ['5184.d1', '7776.u1', '7776.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [41091120, 39366316080, 435], 'label': '46656.ir.2592.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '2592.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.bz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714498
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ha1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1', '864.ce1', '1296.bv1', '1296.cu1', '1296.fk1', '1296.gp1', '1296.ic1', '1296.ie1', '1296.if1'], 'contains': ['5184.j1', '7776.x1', '7776.y1', '7776.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 269279866800, 37885034880], 'label': '46656.ir.2592.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '2592.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714499
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1', '864.cf1', '1296.o1', '1296.bw1', '1296.cv1', '1296.gq1', '1296.ib1', '1296.id1', '1296.ig1'], 'contains': ['5184.m1', '7776.x1', '7776.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 268280812800, 37885034880], 'label': '46656.ir.2592.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '2592.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cd1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714500
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.a1', '864.cg1', '864.ch1', '864.ci1', '1296.cw1', '1296.gr1', '1296.ih1'], 'contains': ['5184.n1', '7776.y1', '7776.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091120, 39366316080, 269279866800], 'label': '46656.ir.2592.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '2592.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ce1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714501
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cj1', '864.ck1', '864.cm1', '1296.bk1', '1296.bu1', '1296.ep1', '1296.gj1', '1296.ij1', '1296.ik1', '1296.il1', '1296.ip1', '1296.ir1', '1296.iu1', '1296.ix1', '1296.iy1', '1296.iz1', '1296.ja1', '1296.kc1'], 'contains': ['5184.b1', '7776.ba1', '7776.bb1', '7776.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 1481684400, 1521641624], 'label': '46656.ir.2592.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '2592.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714502
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cj1', '864.cl1', '864.cn1', '1296.bl1', '1296.gk1', '1296.im1', '1296.is1', '1296.iv1', '1296.jb1', '1296.jc1'], 'contains': ['5184.e1', '7776.ba1', '7776.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1481684725, 39957120, 39957224], 'label': '46656.ir.2592.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '2592.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714503
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cj1', '864.co1', '864.cp1', '1296.l1', '1296.bm1', '1296.ez1', '1296.gl1', '1296.ii1', '1296.in1', '1296.io1', '1296.iq1', '1296.it1', '1296.iw1', '1296.jd1', '1296.je1', '1296.jf1', '1296.jg1', '1296.kb1'], 'contains': ['5184.a1', '7776.ba1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 325, 39957224], 'label': '46656.ir.2592.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '2592.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ch1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714504
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ck1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cl1', '864.cm1', '864.co1', '864.cq1', '1296.m1', '1296.ck1', '1296.eq1', '1296.jj1', '1296.jq1', '1296.jt1', '1296.kc1'], 'contains': ['5184.b1', '7776.ba1', '7776.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39957120, 31697930984, 37885034880], 'label': '46656.ir.2592.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bn1', 'old_label': '2592.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ci1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714505
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1', '18.b1', '18.i1', '18.w1'], 'contains': ['72.er1', '72.ey1', '72.fa1', '324.dm1', '324.eo1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 1174320, 1174645, 7, 39957619], 'label': '46656.ir.36.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cz1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714506
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ck1', '864.cn1', '864.cp1', '864.cq1', '1296.n1', '1296.er1', '1296.hk1', '1296.jh1', '1296.jk1', '1296.js1', '1296.jw1'], 'contains': ['5184.d1', '7776.ba1', '7776.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39957555, 387037284480, 39957120], 'label': '46656.ir.2592.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '2592.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714507
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.fm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ck1', '864.cs1', '1296.bv1', '1296.cx1', '1296.hl1', '1296.ji1', '1296.jl1', '1296.jr1', '1296.jx1'], 'contains': ['5184.j1', '7776.bb1', '7776.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 1481684400], 'label': '46656.ir.2592.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '2592.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ck1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714508
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cl1', '864.cm1', '864.cr1', '1296.cl1', '1296.jm1', '1296.ju1'], 'contains': ['5184.k1', '7776.bc1', '7776.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39957120, 37885034880, 1521641624], 'label': '46656.ir.2592.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '2592.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714509
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cm1', '864.cs1', '1296.bw1', '1296.cm1', '1296.cy1', '1296.jn1', '1296.jp1', '1296.jv1', '1296.kn1'], 'contains': ['5184.m1', '7776.bb1', '7776.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400], 'label': '46656.ir.2592.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '2592.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714510
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ck1', '864.cn1', '864.cr1', '1296.hm1', '1296.jo1', '1296.jy1'], 'contains': ['5184.u1', '7776.bc1', '7776.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [387037284480, 39957120, 1521641624], 'label': '46656.ir.2592.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '2592.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714511
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cq1', '864.cr1', '864.cs1', '1296.o1', '1296.cn1', '1296.cz1', '1296.hn1', '1296.kd1', '1296.ke1', '1296.kf1', '1296.kg1', '1296.kh1', '1296.ki1', '1296.kj1', '1296.kk1', '1296.kl1', '1296.km1', '1296.kn1'], 'contains': ['5184.m1', '7776.bd1', '7776.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 39957120, 37885034880], 'label': '46656.ir.2592.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '2592.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.co1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714512
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ct1', '864.cu1', '864.cw1', '864.cx1', '1296.f1', '1296.es1', '1296.gn1', '1296.jh1', '1296.ko1', '1296.kq1', '1296.kt1'], 'contains': ['5184.d1', '7776.bf1', '7776.bg1', '7776.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 6267744000, 435], 'label': '46656.ir.2592.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '2592.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714513
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ct1', '864.cv1', '864.cy1', '864.cz1', '1296.g1', '1296.kr1', '1296.ku1'], 'contains': ['5184.g1', '7776.bf1', '7776.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316184, 325, 6267744000], 'label': '46656.ir.2592.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.p1', 'old_label': '2592.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714514
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ct1', '864.da1', '864.db1', '864.dc1', '864.dd1', '1296.h1', '1296.fa1', '1296.fg1', '1296.ii1', '1296.kp1', '1296.ks1', '1296.kv1'], 'contains': ['5184.a1', '7776.bf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [325, 104, 6267744000], 'label': '46656.ir.2592.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '2592.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cr1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714515
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ht1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cu1', '864.cv1', '864.da1', '864.de1', '1296.bq1', '1296.et1', '1296.fh1', '1296.ij1', '1296.kz1', '1296.la1', '1296.lk1'], 'contains': ['5184.b1', '7776.bf1', '7776.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [355419187635, 268280812800, 6267744000], 'label': '46656.ir.2592.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '2592.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714516
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '18.c1', '18.f1', '18.w1'], 'contains': ['72.es1', '72.et1', '72.fa1', '324.dn1', '324.ep1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 499, 7, 6227464327], 'label': '46656.ir.36.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.da1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714517
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cx1', '864.cy1', '864.db1', '864.de1', '864.df1', '864.dg1', '1296.eu1', '1296.fi1', '1296.lb1'], 'contains': ['5184.c1', '7776.bf1', '7776.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [301891126320, 104, 6267744000], 'label': '46656.ir.2592.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.dh1', 'old_label': '2592.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ct1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714518
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cw1', '864.cz1', '864.dc1', '864.de1', '1296.i1', '1296.ev1', '1296.fj1', '1296.jh1', '1296.ky1', '1296.lc1', '1296.ln1'], 'contains': ['5184.d1', '7776.bf1', '7776.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 40323593520, 6267744000], 'label': '46656.ir.2592.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '2592.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714519
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jv1', '864.dd1', '864.df1', '1296.ew1', '1296.gm1', '1296.lj1'], 'contains': ['5184.h1', '7776.bf1', '7776.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [104, 6267744000, 655807627521], 'label': '46656.ir.2592.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fx1', 'old_label': '2592.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714520
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.fs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cu1', '864.di1', '1296.br1', '1296.da1', '1296.gp1', '1296.ji1', '1296.kx1', '1296.ld1', '1296.ll1'], 'contains': ['5184.j1', '7776.bg1', '7776.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 6267744000], 'label': '46656.ir.2592.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '2592.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714521
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cu1', '864.cv1', '864.dh1', '1296.bs1', '1296.le1', '1296.lm1'], 'contains': ['5184.l1', '7776.bh1', '7776.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 387999647384, 6267744000], 'label': '46656.ir.2592.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '2592.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714522
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cw1', '864.di1', '1296.j1', '1296.db1', '1296.gq1', '1296.kd1', '1296.kw1', '1296.lf1', '1296.lo1'], 'contains': ['5184.m1', '7776.bg1', '7776.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 6267744000], 'label': '46656.ir.2592.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '2592.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714523
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.fd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.cx1', '864.di1', '864.dj1', '864.dk1', '1296.dc1', '1296.gr1', '1296.lg1'], 'contains': ['5184.n1', '7776.bg1', '7776.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 269279866800, 6267744000], 'label': '46656.ir.2592.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '2592.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.cz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714524
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cx1', '864.cy1', '864.dh1', '864.dl1', '864.dm1', '1296.lh1'], 'contains': ['5184.p1', '7776.bh1', '7776.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [269279866904, 301891126320, 6267744000], 'label': '46656.ir.2592.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.gy1', 'old_label': '2592.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.da1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714525
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.cw1', '864.cz1', '864.dh1', '1296.k1', '1296.li1', '1296.lp1'], 'contains': ['5184.v1', '7776.bh1', '7776.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684504, 40323593520, 6267744000], 'label': '46656.ir.2592.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '2592.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.db1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714526
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.de1', '864.dh1', '864.di1', '1296.bt1', '1296.dd1', '1296.fk1', '1296.ji1', '1296.lq1', '1296.lr1', '1296.lt1'], 'contains': ['5184.j1', '7776.bi1', '7776.bj1', '7776.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 40323593520, 6267744000], 'label': '46656.ir.2592.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '2592.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714527
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '18.c1', '18.h1', '18.u1'], 'contains': ['72.es1', '72.ew1', '72.fb1', '324.do1', '324.eq1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 499, 7], 'label': '46656.ir.36.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.db1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714528
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.df1', '864.dj1', '864.dl1', '1296.de1', '1296.go1', '1296.ls1'], 'contains': ['5184.q1', '7776.bj1', '7776.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [301891126320, 655477406640, 6267744000], 'label': '46656.ir.2592.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '2592.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dd1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714529
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dg1', '864.dk1', '864.dm1', '1296.df1'], 'contains': ['5184.s1', '7776.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [301891126320, 623823424560, 6267744000], 'label': '46656.ir.2592.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '2592.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.de1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216714530
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dn1', '864.do1', '864.dp1', '1296.b1', '1296.bx1', '1296.gs1', '1296.ib1', '1296.jp1', '1296.ke1', '1296.kw1'], 'contains': ['5184.m1', '7776.bm1', '7776.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400], 'label': '46656.ir.2592.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '2592.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.df1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216714531
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.cm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dn1', '864.dr1', '864.ds1', '864.du1', '1296.c1', '1296.p1', '1296.by1', '1296.hs1', '1296.ik1', '1296.jj1', '1296.jq1'], 'contains': ['5184.b1', '7776.bm1', '7776.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 31658054504, 37885034880], 'label': '46656.ir.2592.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '2592.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714532
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dn1', '864.dq1', '864.dt1', '864.dv1', '1296.d1', '1296.fl1', '1296.gt1', '1296.ht1', '1296.jk1', '1296.ko1', '1296.ky1'], 'contains': ['5184.d1', '7776.bn1', '7776.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 39366316080, 104], 'label': '46656.ir.2592.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '2592.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714533
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ee1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dp1', '864.dq1', '1296.bn1', '1296.fm1', '1296.gu1', '1296.ic1', '1296.jl1', '1296.kx1', '1296.lq1'], 'contains': ['5184.j1', '7776.bn1', '7776.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800], 'label': '46656.ir.2592.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '2592.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.di1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714534
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.do1', '864.dr1', '864.ds1', '1296.q1', '1296.bz1', '1296.jm1'], 'contains': ['5184.k1', '7776.bm1', '7776.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39916807, 299935198184, 37885034880], 'label': '46656.ir.2592.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.di1', 'old_label': '2592.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714535
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dp1', '864.ds1', '1296.r1', '1296.bo1', '1296.ca1', '1296.id1', '1296.jn1', '1296.jp1', '1296.kf1'], 'contains': ['5184.m1', '7776.bm1', '7776.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916807, 268280812800, 37885034880], 'label': '46656.ir.2592.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.z1', 'old_label': '2592.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714536
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.do1', '864.dq1', '864.dt1', '1296.fn1', '1296.gv1', '1296.jo1'], 'contains': ['5184.u1', '7776.bn1', '7776.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812904], 'label': '46656.ir.2592.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iu1', 'old_label': '2592.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714557
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jz1', '864.ef1', '864.eq1', '1296.ek1', '1296.hp1', '1296.lj1'], 'contains': ['5184.h1', '7776.bu1', '7776.bx1', '7776.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [623710972161, 6227827207, 104], 'label': '46656.ir.2592.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '2592.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ed1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714537
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dq1', '864.ds1', '864.dw1', '1296.s1', '1296.bp1', '1296.fo1', '1296.hu1', '1296.il1', '1296.jq1', '1296.kz1'], 'contains': ['5184.b1', '7776.bo1', '7776.bp1', '7776.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 355419187635, 268280812800], 'label': '46656.ir.2592.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '2592.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714538
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '18.c1', '18.g1', '18.x1'], 'contains': ['72.et1', '72.eu1', '72.fb1', '324.dp1', '324.er1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6267381738, 6227464327], 'label': '46656.ir.36.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dc1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714539
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dr1', '864.dt1', '864.dw1', '1296.t1', '1296.fp1', '1296.im1'], 'contains': ['5184.e1', '7776.bo1', '7776.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 268280813125, 355419187304], 'label': '46656.ir.2592.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '2592.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dn1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714540
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.du1', '864.dv1', '864.dw1', '1296.e1', '1296.u1', '1296.fq1', '1296.ho1', '1296.in1', '1296.io1', '1296.kp1'], 'contains': ['5184.a1', '7776.bo1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 325, 104], 'label': '46656.ir.2592.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '2592.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.do1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714541
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dx1', '864.dy1', '864.dz1', '1296.cb1', '1296.co1', '1296.gw1', '1296.ie1', '1296.jr1', '1296.kx1', '1296.lr1'], 'contains': ['5184.j1', '7776.br1', '7776.bs1', '7776.bt1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827207], 'label': '46656.ir.2592.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '2592.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714542
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.hl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dx1', '864.ea1', '864.eb1', '864.ei1', '1296.cc1', '1296.eg1', '1296.fr1', '1296.hv1', '1296.ip1', '1296.kz1', '1296.la1'], 'contains': ['5184.b1', '7776.br1', '7776.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268280812800, 355419187304, 6227827207], 'label': '46656.ir.2592.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '2592.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714543
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dx1', '864.ed1', '864.ee1', '864.ef1', '864.eg1', '864.ej1', '1296.eh1', '1296.hw1', '1296.lb1'], 'contains': ['5184.c1', '7776.bs1', '7776.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387999647280, 387999647715, 6227827207], 'label': '46656.ir.2592.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ex1', 'old_label': '2592.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714544
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dx1', '864.ec1', '864.eh1', '864.ek1', '1296.v1', '1296.ei1', '1296.gx1', '1296.hx1', '1296.js1', '1296.ko1', '1296.lc1'], 'contains': ['5184.d1', '7776.bt1', '7776.bu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 6227827207, 104], 'label': '46656.ir.2592.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '2592.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ds1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714545
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ea1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dz1', '864.ea1', '1296.cd1', '1296.cp1', '1296.fs1', '1296.if1', '1296.jr1', '1296.ld1', '1296.lq1'], 'contains': ['5184.j1', '7776.br1', '7776.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 40323593520, 6227827207], 'label': '46656.ir.2592.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '2592.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714546
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dy1', '864.ea1', '864.eb1', '1296.ce1', '1296.ft1', '1296.le1'], 'contains': ['5184.l1', '7776.br1', '7776.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [268280812800, 40323593955, 6227827207], 'label': '46656.ir.2592.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '2592.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.du1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714547
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dz1', '864.ec1', '1296.w1', '1296.cq1', '1296.gy1', '1296.ig1', '1296.kg1', '1296.kw1', '1296.lf1'], 'contains': ['5184.m1', '7776.bt1', '7776.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1481684400, 6227827207], 'label': '46656.ir.2592.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '2592.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714548
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.dg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.dz1', '864.ed1', '864.el1', '864.em1', '1296.cr1', '1296.ih1', '1296.lg1'], 'contains': ['5184.n1', '7776.bs1', '7776.bv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [40323593520, 269279866800, 6227827207], 'label': '46656.ir.2592.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cr1', 'old_label': '2592.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714549
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.f1', '12.h1', '12.l1', '12.m1', '12.n1', '12.o1', '12.t1', '12.u1', '12.w1', '12.ba1', '12.bj1', '12.bx1', '12.ca1', '12.cc1', '18.j1', '18.p1', '54.q1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.6.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714550
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '18.d1', '18.f1', '18.x1'], 'contains': ['72.et1', '72.ev1', '72.ex1', '324.dq1', '324.es1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6227827818, 6227464327], 'label': '46656.ir.36.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dd1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714551
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dy1', '864.ed1', '864.ee1', '864.en1', '864.eo1', '1296.lh1'], 'contains': ['5184.p1', '7776.bs1', '7776.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [387999647280, 40323593955, 6227827207], 'label': '46656.ir.2592.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ly1', 'old_label': '2592.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714552
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ef1', '864.el1', '864.en1', '1296.cs1', '1296.hy1', '1296.ls1'], 'contains': ['5184.q1', '7776.bs1', '7776.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [624302466480, 300933848880, 6227827207], 'label': '46656.ir.2592.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '2592.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dy1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714553
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ef1', '864.eg1', '864.em1', '864.en1', '864.eo1', '1296.hz1'], 'contains': ['5184.r1', '7776.bs1', '7776.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [387999647280, 6227827207, 463289990028], 'label': '46656.ir.2592.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hz1', 'old_label': '2592.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.dz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714554
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.dy1', '864.ec1', '864.eh1', '1296.x1', '1296.gz1', '1296.li1'], 'contains': ['5184.v1', '7776.bt1', '7776.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316080, 1481684504, 6227827207], 'label': '46656.ir.2592.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '2592.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ea1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714555
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ea1', '864.ec1', '864.ed1', '864.ep1', '1296.y1', '1296.ej1', '1296.fu1', '1296.ia1', '1296.js1', '1296.kq1', '1296.ky1'], 'contains': ['5184.d1', '7776.bu1', '7776.bv1', '7776.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [40323593624, 40323593520, 6227827207], 'label': '46656.ir.2592.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '2592.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714556
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.eb1', '864.ee1', '864.eh1', '864.ep1', '1296.z1', '1296.fv1', '1296.kr1'], 'contains': ['5184.g1', '7776.bu1', '7776.bw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593845, 33139370984, 6227827207], 'label': '46656.ir.2592.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '2592.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ec1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714558
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.ka1', '864.eg1', '864.eq1', '1296.hq1'], 'contains': ['5184.i1', '7776.bu1', '7776.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [455107081395, 6227827207, 104], 'label': '46656.ir.2592.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ie1', 'old_label': '2592.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ee1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714559
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ei1', '864.ej1', '864.ek1', '864.ep1', '864.eq1', '1296.ba1', '1296.ex1', '1296.fw1', '1296.hr1', '1296.iq1', '1296.kp1', '1296.ks1'], 'contains': ['5184.a1', '7776.bu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [325, 6227827207, 104], 'label': '46656.ir.2592.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '2592.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ef1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714560
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bd1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.er1', '864.es1', '864.et1', '864.eu1', '864.ev1', '1296.p1', '1296.cf1', '1296.ep1', '1296.fr1', '1296.hu1', '1296.jt1', '1296.lk1'], 'contains': ['5184.b1', '7776.bz1', '7776.ca1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1481684835, 1481684400, 39957127], 'label': '46656.ir.2592.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '2592.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714561
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '18.d1', '18.g1', '18.w1'], 'contains': ['72.et1', '72.ey1', '72.ez1', '324.dr1', '324.et1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 7, 39957619, 6227464327], 'label': '46656.ir.36.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.de1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714562
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.er1', '864.ew1', '864.ez1', '1296.cg1', '1296.cx1', '1296.fs1', '1296.gw1', '1296.ic1', '1296.ll1', '1296.lt1'], 'contains': ['5184.j1', '7776.bz1', '7776.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [301891126320, 1481684400, 39957127], 'label': '46656.ir.2592.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '2592.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714563
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.et1', '864.eu1', '864.ew1', '864.ex1', '864.ex2', '864.ey1', '1296.q1', '1296.ch1', '1296.ju1'], 'contains': ['5184.k1', '7776.bz1', '7776.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 1481684400, 39957127], 'label': '46656.ir.2592.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '2592.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ei1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714564
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.er1', '864.es1', '864.ew1', '864.ex1', '864.ex2', '864.ey1', '1296.ci1', '1296.ft1', '1296.lm1'], 'contains': ['5184.l1', '7776.bz1', '7776.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [294706903784, 1481684400, 39957127], 'label': '46656.ir.2592.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '2592.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ej1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714565
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.eu1', '864.ey1', '864.ez1', '1296.r1', '1296.bx1', '1296.cj1', '1296.cy1', '1296.id1', '1296.jv1', '1296.kh1'], 'contains': ['5184.m1', '7776.bz1', '7776.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957127], 'label': '46656.ir.2592.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '2592.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ek1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714566
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.eu1', '864.fa1', '864.fb1', '864.fd1', '1296.s1', '1296.bb1', '1296.by1', '1296.eq1', '1296.hs1', '1296.ir1', '1296.jt1'], 'contains': ['5184.b1', '7776.ca1', '7776.cb1', '7776.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [31658054504, 39957127, 37885034880], 'label': '46656.ir.2592.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cl1', 'old_label': '2592.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.el1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714567
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.er1', '864.fb1', '864.fc1', '864.fe1', '1296.bc1', '1296.er1', '1296.fu1', '1296.gx1', '1296.ht1', '1296.kt1', '1296.ln1'], 'contains': ['5184.d1', '7776.ca1', '7776.cc1', '7776.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [387037284480, 39957127, 435], 'label': '46656.ir.2592.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '2592.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.em1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714568
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.et1', '864.fa1', '864.fc1', '864.fd1', '1296.t1', '1296.bd1', '1296.is1'], 'contains': ['5184.e1', '7776.ca1', '7776.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [31658054504, 39957127, 37885035205], 'label': '46656.ir.2592.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cw1', 'old_label': '2592.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.en1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714569
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.es1', '864.fa1', '864.fc1', '864.fe1', '1296.be1', '1296.fv1', '1296.ku1'], 'contains': ['5184.g1', '7776.ca1', '7776.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [293708217925, 39957127, 104], 'label': '46656.ir.2592.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.by1', 'old_label': '2592.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eo1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714570
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ev1', '864.fd1', '864.fe1', '1296.u1', '1296.bf1', '1296.ez1', '1296.fw1', '1296.ho1', '1296.it1', '1296.kv1', '1296.lu1', '1296.lv1'], 'contains': ['5184.a1', '7776.ca1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [325, 39957127, 104], 'label': '46656.ir.2592.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '2592.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ep1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714571
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ey1', '864.fa1', '864.fb1', '1296.bg1', '1296.bz1', '1296.ju1'], 'contains': ['5184.k1', '7776.cb1', '7776.cd1', '7776.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [299935198515, 39957127, 37885034880], 'label': '46656.ir.2592.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.di1', 'old_label': '2592.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714572
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '18.c1', '18.i1', '18.v1'], 'contains': ['72.eu1', '72.ew1', '72.fa1', '324.ds1', '324.eu1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39917299, 39366316080, 6267381127, 7, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.36.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.df1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714573
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ez1', '864.fb1', '1296.bh1', '1296.ca1', '1296.cz1', '1296.gy1', '1296.ib1', '1296.jv1', '1296.lo1', '1296.lw1', '1296.lx1'], 'contains': ['5184.m1', '7776.cb1', '7776.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957127, 37885034880], 'label': '46656.ir.2592.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '2592.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.er1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714574
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ew1', '864.fb1', '864.fc1', '1296.bi1', '1296.gz1', '1296.lp1'], 'contains': ['5184.v1', '7776.cc1', '7776.cd1', '7776.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [268280813235, 387037284480, 39957127], 'label': '46656.ir.2592.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '2592.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.es1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714575
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ex1', '864.fa1', '864.fc1', '1296.bj1'], 'contains': ['5184.y1', '7776.cd1', '7776.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [355419187304, 39957127, 37885035205], 'label': '46656.ir.2592.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.cf1', 'old_label': '2592.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.et1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714576
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.et2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ex2', '864.fa1', '864.fc1', '1296.bj2', '1296.ly1', '1296.lz1'], 'contains': ['5184.y2', '7776.cd1', '7776.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [387037284584, 39957127, 37885035205], 'label': '46656.ir.2592.et2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cs1', 'old_label': '2592.et2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.et2', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714577
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.jx1', '864.ff1', '864.fg1', '864.fh1', '1296.el1', '1296.ha1', '1296.lj1'], 'contains': ['5184.h1', '7776.cf1', '7776.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [93536397441, 104, 41091127], 'label': '46656.ir.2592.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '2592.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.eu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714578
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cs1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ff1', '864.fi1', '864.fj1', '1296.ct1', '1296.hb1', '1296.ls1'], 'contains': ['5184.q1', '7776.cf1', '7776.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [301891126320, 655477406640, 41091127], 'label': '46656.ir.2592.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '2592.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ev1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714579
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ff1', '864.fg1', '1296.hc1'], 'contains': ['5184.ba1', '7776.cf1', '7776.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [655807627898, 294706904005, 41091127], 'label': '46656.ir.2592.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hc1', 'old_label': '2592.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ew1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714580
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fk1', '864.fl1', '864.fm1', '864.fn1', '864.fu1', '1296.bb1', '1296.cf1', '1296.em1', '1296.fx1', '1296.il1', '1296.jj1', '1296.la1'], 'contains': ['5184.b1', '7776.cg1', '7776.ch1', '7776.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [31658054504, 37885034880, 41091127], 'label': '46656.ir.2592.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '2592.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ex1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714581
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ff1', '864.fk1', '864.fo1', '864.fp1', '864.fq1', '864.fv1', '1296.en1', '1296.fy1', '1296.lb1'], 'contains': ['5184.c1', '7776.cg1', '7776.ci1', '7776.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [301891126320, 41091127, 435], 'label': '46656.ir.2592.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ey1', 'old_label': '2592.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ey1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714582
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fk1', '864.fn1', '864.fo1', '864.fr1', '864.fs1', '864.ft1', '864.fw1', '1296.bc1', '1296.eo1', '1296.fz1', '1296.hd1', '1296.jk1', '1296.kq1', '1296.lc1'], 'contains': ['5184.d1', '7776.cg1', '7776.cj1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39366316080, 41091127, 435], 'label': '46656.ir.2592.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '2592.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ez1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714583
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '18.d1', '18.h1', '18.v1'], 'contains': ['72.ev1', '72.ew1', '72.ez1', '324.dt1', '324.ev1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 40819, 7], 'label': '46656.ir.36.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dg1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714584
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fm1', '864.fp1', '864.fr1', '864.fs1', '864.fu1', '1296.bd1', '1296.ga1', '1296.im1'], 'contains': ['5184.e1', '7776.cg1', '7776.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [268280812904, 355419187525, 41091127], 'label': '46656.ir.2592.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.be1', 'old_label': '2592.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fa1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714585
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fg1', '864.fl1', '864.fp1', '864.fr1', '864.ft1', '864.fv1', '1296.gb1'], 'contains': ['5184.f1', '7776.cg1', '7776.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [381772702184, 301891126645, 41091127], 'label': '46656.ir.2592.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hd1', 'old_label': '2592.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fb1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714586
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fl1', '864.fm1', '864.fp1', '864.fq1', '864.fs1', '864.ft1', '864.fw1', '1296.be1', '1296.gc1', '1296.kr1'], 'contains': ['5184.g1', '7776.cg1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 325, 41091127], 'label': '46656.ir.2592.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.r1', 'old_label': '2592.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714587
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fh1', '864.fu1', '864.fv1', '864.fw1', '1296.bf1', '1296.ey1', '1296.gd1', '1296.in1', '1296.ks1'], 'contains': ['5184.a1', '7776.cg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [325, 104, 41091127], 'label': '46656.ir.2592.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '2592.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fd1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714588
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fk1', '864.fx1', '864.ga1', '1296.cg1', '1296.cu1', '1296.ge1', '1296.he1', '1296.jl1', '1296.ld1', '1296.lr1'], 'contains': ['5184.j1', '7776.ch1', '7776.ci1', '7776.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [269279866800, 37885034880, 41091127], 'label': '46656.ir.2592.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '2592.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fe1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714589
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fm1', '864.fn1', '864.fx1', '864.fy1', '864.fy2', '864.fz1', '1296.bg1', '1296.ch1', '1296.jm1'], 'contains': ['5184.k1', '7776.ch1', '7776.ck1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [1481684835, 37885034880, 41091127], 'label': '46656.ir.2592.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '2592.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ff1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714590
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fk1', '864.fl1', '864.fx1', '864.fy1', '864.fy2', '864.fz1', '1296.ci1', '1296.gf1', '1296.le1'], 'contains': ['5184.l1', '7776.ch1', '7776.cl1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [37885034880, 41091127, 270715783395], 'label': '46656.ir.2592.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '2592.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714591
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fn1', '864.fz1', '864.ga1', '1296.bh1', '1296.cj1', '1296.cv1', '1296.hf1', '1296.jn1', '1296.ke1', '1296.lf1'], 'contains': ['5184.m1', '7776.ch1', '7776.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [268280812800, 37885034880, 41091127], 'label': '46656.ir.2592.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '2592.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fh1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216714592
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.fi1', '864.fo1', '864.ga1', '864.gb1', '1296.cw1', '1296.hg1', '1296.lg1'], 'contains': ['5184.n1', '7776.ci1', '7776.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 269279866800, 41091127], 'label': '46656.ir.2592.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '2592.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fi1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714593
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fk1', '864.fp1', '864.fx1', '864.gb1', '864.gc1', '1296.gg1'], 'contains': ['5184.o1', '7776.ci1', '7776.ck1', '7776.cl1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [1481684835, 301891126320, 41091127], 'label': '46656.ir.2592.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.gg1', 'old_label': '2592.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fj1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714594
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '18.d1', '18.i1', '18.u1'], 'contains': ['72.ew1', '72.ex1', '72.ey1', '324.du1', '324.ew1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 7, 39957619], 'label': '46656.ir.36.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dh1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714595
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fj1', '864.fo1', '864.fq1', '864.fx1', '864.gc1', '1296.lh1'], 'contains': ['5184.p1', '7776.ci1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [301891126320, 269279867235, 41091127], 'label': '46656.ir.2592.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.mc1', 'old_label': '2592.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fk1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714596
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fk1', '864.fr1', '864.fz1', '864.gb1', '864.gd1', '864.gd2', '1296.gh1', '1296.hh1', '1296.jo1'], 'contains': ['5184.u1', '7776.cj1', '7776.ck1', '7776.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [355419187635, 39366316080, 41091127], 'label': '46656.ir.2592.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '2592.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714597
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fn1', '864.fs1', '864.fx1', '864.gb1', '864.gd1', '864.gd2', '1296.bi1', '1296.hi1', '1296.li1'], 'contains': ['5184.v1', '7776.cj1', '7776.ck1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091127], 'label': '46656.ir.2592.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '2592.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714598
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fo1', '864.ft1', '864.fx1', '864.fz1', '864.gb1', '864.gd1', '864.gd2', '1296.hj1'], 'contains': ['5184.w1', '7776.cj1', '7776.cl1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [39366316080, 270715783064, 41091127], 'label': '46656.ir.2592.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hj1', 'old_label': '2592.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714599
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['864.fl1', '864.fp1', '864.fr1', '864.fy1', '864.gc1', '864.gd1', '864.gd2', '1296.gi2'], 'contains': ['5184.x1', '7776.ck1', '7776.cl1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 5184, 'diagramx': None, 'generators': [270715783064, 301891126645, 41091127], 'label': '46656.ir.2592.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.gi2', 'old_label': '2592.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fo1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714600
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fo2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fl1', '864.fp1', '864.fr1', '864.fy2', '864.gc1', '864.gd1', '864.gd2', '1296.gi1'], 'contains': ['5184.x2', '7776.ck1', '7776.cl1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [301891126645, 33139370984, 41091127], 'label': '46656.ir.2592.fo2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.gi1', 'old_label': '2592.fo2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fo2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714601
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fm1', '864.fs1', '864.fy1', '864.gc1', '864.gd2', '1296.bj1'], 'contains': ['5184.y1', '7776.ck1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [40323593624, 39366316405, 41091127], 'label': '46656.ir.2592.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.bj1', 'old_label': '2592.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fp1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714602
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fm1', '864.fs1', '864.fy2', '864.gc1', '864.gd1', '1296.bj2'], 'contains': ['5184.y2', '7776.ck1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [356381953304, 355419187525, 41091127], 'label': '46656.ir.2592.fp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.bl1', 'old_label': '2592.fp2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fp2', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714603
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.fq1', '864.ft1', '864.fy1', '864.fy2', '864.gc1', '864.gd1', '864.gd2'], 'contains': ['5184.z1', '7776.cl1', '7776.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 5184, 'diagramx': None, 'generators': [269279866904, 39366316405, 41091127], 'label': '46656.ir.2592.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2592.fq1', 'old_label': '2592.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fq1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714604
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ge1', '864.gf1', '864.gg1', '864.gh1', '864.gi1', '864.gj1', '864.gk1', '1296.v1', '1296.es1', '1296.fl1', '1296.hd1', '1296.ia1', '1296.jw1', '1296.ln1'], 'contains': ['5184.d1', '7776.cn1', '7776.co1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 39366316080, 435], 'label': '46656.ir.2592.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '2592.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714605
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1', '18.j1', '18.w1', '18.x1'], 'contains': ['72.er1', '72.et1', '72.fc1', '72.gn1', '72.he1', '72.hf1', '72.hi1', '108.dr1', '324.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 7, 41051125, 1521641624], 'label': '46656.ir.36.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.di1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714606
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.ge1', '864.gl1', '864.gn1', '1296.cb1', '1296.da1', '1296.fm1', '1296.he1', '1296.if1', '1296.jx1', '1296.lt1'], 'contains': ['5184.j1', '7776.cn1', '7776.cp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800], 'label': '46656.ir.2592.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '2592.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714607
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.gf1', '864.gm1', '864.gn1', '1296.w1', '1296.db1', '1296.gs1', '1296.hf1', '1296.ig1', '1296.ki1', '1296.lo1'], 'contains': ['5184.m1', '7776.cn1', '7776.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684400], 'label': '46656.ir.2592.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '2592.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ft1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714608
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.gg1', '864.gn1', '864.go1', '864.gp1', '864.gq1', '864.gr1', '864.gs1', '1296.dc1', '1296.hg1', '1296.ih1'], 'contains': ['5184.n1', '7776.cn1', '7776.cq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 39366316080, 269279866800], 'label': '46656.ir.2592.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '2592.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714609
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ge1', '864.gh1', '864.gm1', '864.go1', '864.gt1', '864.gt2', '1296.fn1', '1296.hh1', '1296.jy1'], 'contains': ['5184.u1', '7776.cn1', '7776.cs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 355419187635, 39366316080], 'label': '46656.ir.2592.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '2592.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714610
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gf1', '864.gi1', '864.gl1', '864.go1', '864.gt1', '864.gt2', '1296.x1', '1296.hi1', '1296.lp1'], 'contains': ['5184.v1', '7776.cn1', '7776.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684835], 'label': '46656.ir.2592.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '2592.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714611
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gg1', '864.gj1', '864.gl1', '864.gm1', '864.go1', '864.gt1', '864.gt2', '1296.hj1'], 'contains': ['5184.w1', '7776.cn1', '7776.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [6267744007, 39366316080, 270715783395], 'label': '46656.ir.2592.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hj1', 'old_label': '2592.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714612
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.ge1', '864.gu1', '864.gv1', '864.hd1', '1296.cc1', '1296.et1', '1296.fo1', '1296.fx1', '1296.hv1', '1296.iu1', '1296.lk1'], 'contains': ['5184.b1', '7776.co1', '7776.cp1', '7776.cs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 268280812800, 355419187304], 'label': '46656.ir.2592.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '2592.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714613
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gg1', '864.gu1', '864.gw1', '864.gx1', '864.gy1', '864.gz1', '864.ha1', '864.he1', '1296.eu1', '1296.fy1', '1296.hw1'], 'contains': ['5184.c1', '7776.co1', '7776.cq1', '7776.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 301891126320, 104], 'label': '46656.ir.2592.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.fb1', 'old_label': '2592.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.fz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714614
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gf1', '864.gu1', '864.hb1', '864.hf1', '1296.y1', '1296.ev1', '1296.fz1', '1296.gt1', '1296.hx1', '1296.jw1', '1296.kt1'], 'contains': ['5184.d1', '7776.co1', '7776.cr1', '7776.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 40323593955, 40323593520], 'label': '46656.ir.2592.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '2592.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ga1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714615
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gh1', '864.gw1', '864.hb1', '864.hd1', '1296.fp1', '1296.ga1', '1296.iv1'], 'contains': ['5184.e1', '7776.co1', '7776.cs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 268280813125, 355419187304], 'label': '46656.ir.2592.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iq1', 'old_label': '2592.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gb1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714616
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '18.k1', '18.u1', '18.w1'], 'contains': ['72.en1', '72.eq1', '72.es1', '72.ey1', '72.fc1', '108.fc1', '324.dw1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050800, 39957120, 268280812800, 37885034880, 499, 7, 41051125, 31697930984], 'label': '46656.ir.36.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dj1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714617
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gj1', '864.gv1', '864.gw1', '864.hb1', '864.hc1', '864.he1', '1296.gb1'], 'contains': ['5184.f1', '7776.co1', '7776.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 294706904005, 104], 'label': '46656.ir.2592.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hk1', 'old_label': '2592.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gc1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714618
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gi1', '864.gv1', '864.gw1', '864.hf1', '1296.z1', '1296.gc1', '1296.ku1'], 'contains': ['5184.g1', '7776.co1', '7776.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 6267744007, 325], 'label': '46656.ir.2592.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '2592.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gd1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714619
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.kc1', '864.gx1', '864.hc1', '864.hg1', '1296.ew1', '1296.ha1', '1296.hp1'], 'contains': ['5184.h1', '7776.co1', '7776.cv1', '7776.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 104, 655807627521], 'label': '46656.ir.2592.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.gq1', 'old_label': '2592.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.ge1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714620
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['648.kd1', '864.gy1', '864.hc1', '864.hg1', '1296.hq1'], 'contains': ['5184.i1', '7776.co1', '7776.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [6267744007, 325, 462811064028], 'label': '46656.ir.2592.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hq1', 'old_label': '2592.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gf1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714621
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.gk1', '864.hd1', '864.he1', '864.hf1', '864.hg1', '1296.ba1', '1296.fa1', '1296.fq1', '1296.gd1', '1296.hr1', '1296.iw1', '1296.kv1'], 'contains': ['5184.a1', '7776.co1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 325, 104], 'label': '46656.ir.2592.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '2592.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gg1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 216714622
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.gn1', '864.gu1', '1296.cd1', '1296.dd1', '1296.ge1', '1296.gu1', '1296.ie1', '1296.jx1', '1296.ll1'], 'contains': ['5184.j1', '7776.cp1', '7776.cq1', '7776.cr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 268280812800, 40323593520], 'label': '46656.ir.2592.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '2592.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714623
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gl1', '864.gu1', '864.gv1', '1296.ce1', '1296.gf1', '1296.lm1'], 'contains': ['5184.l1', '7776.cp1', '7776.ct1', '7776.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800], 'label': '46656.ir.2592.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '2592.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gi1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714624
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.go1', '864.gu1', '864.gw1', '1296.gg1'], 'contains': ['5184.o1', '7776.cq1', '7776.cs1', '7776.ct1', '7776.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 268280813235, 301891126320], 'label': '46656.ir.2592.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hp1', 'old_label': '2592.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gj1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714625
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.gp1', '864.gx1', '1296.de1', '1296.hb1', '1296.hy1'], 'contains': ['5184.q1', '7776.cq1', '7776.cv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 301891126320, 655477406640], 'label': '46656.ir.2592.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '2592.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gk1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714626
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gq1', '864.gx1', '864.gy1', '1296.hz1'], 'contains': ['5184.r1', '7776.cq1', '7776.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 301891126320, 462811064028], 'label': '46656.ir.2592.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ir1', 'old_label': '2592.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gl1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216714627
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '18.k1', '18.v1', '18.x1'], 'contains': ['72.eo1', '72.ep1', '72.eu1', '72.ev1', '72.fc1', '108.fd1', '324.dx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050800, 39957120, 268280812800, 37885034880, 7, 41051125, 39917299, 31697930984], 'label': '46656.ir.36.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dk1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714628
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.gr1', '864.gz1', '1296.df1'], 'contains': ['5184.s1', '7776.cq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744007, 301891126320, 623823424560], 'label': '46656.ir.2592.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.ew1', 'old_label': '2592.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gm1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216714629
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gs1', '864.gz1', '864.ha1'], 'contains': ['5184.t1', '7776.cq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [6267744007, 722861314944, 388956924720], 'label': '46656.ir.2592.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '864.gs1', 'old_label': '2592.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gn1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 216714630
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gm1', '864.gu1', '864.hb1', '1296.gh1', '1296.gv1', '1296.jy1'], 'contains': ['5184.u1', '7776.cr1', '7776.cs1', '7776.ct1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [6267744007, 294706904115, 40323593520], 'label': '46656.ir.2592.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.iu1', 'old_label': '2592.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.go1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714631
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gt1', '864.gv1', '864.gw1', '864.hb1', '1296.gi1'], 'contains': ['5184.x2', '7776.cs1', '7776.ct1', '7776.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [6267744007, 40323593845, 388956924824], 'label': '46656.ir.2592.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq1', 'old_label': '2592.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gp1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714632
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gp2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['864.gt2', '864.gv1', '864.gw1', '864.hb1', '1296.gi2'], 'contains': ['5184.x1', '7776.cs1', '7776.ct1', '7776.cu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': None, 'generators': [6267744007, 381772702184, 294706904005], 'label': '46656.ir.2592.gp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hq2', 'old_label': '2592.gp2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gp2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714633
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gx1', '864.hc1', '1296.hc1'], 'contains': ['5184.ba1', '7776.ct1', '7776.cv1', '7776.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [388956925045, 6267744007, 655807627898], 'label': '46656.ir.2592.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hc1', 'old_label': '2592.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 216714634
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2592.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['864.gy1', '864.hc1'], 'contains': ['5184.bb1', '7776.ct1', '7776.cw1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 5184, 'diagramx': None, 'generators': [6267744007, 301891126424, 174564190515], 'label': '46656.ir.2592.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2592.gr1', 'old_label': '2592.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.gr1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 216714635
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.j1', '972.a1', '972.c1', '972.ba1', '1458.a1'], 'contains': ['5832.a1', '5832.c1', '5832.e1', '5832.v1', '5832.w1', '5832.bp1', '5832.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [499, 443130957804, 444, 40320], 'label': '46656.ir.2916.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '2916.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714636
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.k1', '972.b1', '972.d1', '972.bb1', '1458.a1'], 'contains': ['5832.a1', '5832.e1', '5832.f1', '5832.x1', '5832.y1', '5832.br1', '5832.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [180790853484, 41051299, 444, 40320], 'label': '46656.ir.2916.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '2916.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714637
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.e1', '972.j1', '972.bc1', '1458.a1', '1458.b1', '1458.i1'], 'contains': ['5832.a1', '5832.b1', '5832.g1', '5832.h1', '5832.j1', '5832.u1', '5832.z1', '5832.bd1', '5832.bt1', '5832.bu1', '5832.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [7, 1174320, 39916800, 6227827207], 'label': '46656.ir.2916.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714638
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1', '18.l1', '18.u1', '18.x1'], 'contains': ['72.ex1', '72.fb1', '72.fc1', '324.dy1', '324.fa1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 7, 41051125, 6227827818, 1521641624], 'label': '46656.ir.36.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dl1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714639
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.m1', '972.f1', '972.h1', '972.be1', '1458.a1', '1458.c1', '1458.j1'], 'contains': ['5832.b1', '5832.c1', '5832.f1', '5832.ba1', '5832.bb1', '5832.be1', '5832.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 499, 39957564, 1134000], 'label': '46656.ir.2916.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714640
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.e1', '972.k1', '972.bf1', '1458.c1', '1458.d1', '1458.i1'], 'contains': ['5832.b1', '5832.k1', '5832.l1', '5832.bf1', '5832.bi1', '5832.cc1', '5832.cd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 7, 1174320, 39916800], 'label': '46656.ir.2916.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714641
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.o1', '972.g1', '972.bg1', '1458.b1', '1458.d1', '1458.j1'], 'contains': ['5832.b1', '5832.d1', '5832.bb1', '5832.bh1', '5832.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 41051299, 39957564, 1134000], 'label': '46656.ir.2916.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714642
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.p1', '972.i1', '972.bh1', '1458.a1', '1458.d1', '1458.k1'], 'contains': ['5832.b1', '5832.e1', '5832.bc1', '5832.bj1', '5832.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 1174320, 39916800, 6227827818], 'label': '46656.ir.2916.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714643
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.h1', '324.q1', '972.bi1', '1458.b1', '1458.c1', '1458.k1'], 'contains': ['5832.b1', '5832.m1', '5832.bm1', '5832.bn1', '5832.by1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 1174320, 39916800, 6267381738], 'label': '46656.ir.2916.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714644
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.s1', '972.l1', '972.bl1', '1458.i1'], 'contains': ['5832.h1', '5832.i1', '5832.l1', '5832.bv1', '5832.bw1', '5832.ca1', '5832.cb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 1174320, 39916800, 39957127], 'label': '46656.ir.2916.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714645
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.u1', '972.m1', '972.bq1', '1458.i1'], 'contains': ['5832.i1', '5832.j1', '5832.k1', '5832.ce1', '5832.cf1', '5832.cg1', '5832.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [1174320, 39916800, 6227827207, 39957127], 'label': '46656.ir.2916.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714646
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ch1', '972.n1', '972.t1', '1458.e1', '1458.f1', '1458.i1'], 'contains': ['5832.n1', '5832.o1', '5832.r1', '5832.z1', '5832.bf1', '5832.bv1', '5832.ce1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [7, 1174320, 40320, 6227827207], 'label': '46656.ir.2916.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '2916.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714647
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ci1', '972.o1', '972.u1', '1458.g1', '1458.h1', '1458.i1'], 'contains': ['5832.n1', '5832.p1', '5832.s1', '5832.bd1', '5832.bi1', '5832.ca1', '5832.cf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 7, 1174320, 40320], 'label': '46656.ir.2916.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714648
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.z1', '972.p1', '972.br1', '1458.e1', '1458.g1', '1458.j1'], 'contains': ['5832.c1', '5832.d1', '5832.n1', '5832.be1', '5832.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 499, 39957564, 39916800], 'label': '46656.ir.2916.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '2916.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714649
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1', '18.l1', '18.v1', '18.w1'], 'contains': ['72.ez1', '72.fa1', '72.fc1', '324.dz1', '324.fb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6267744618, 7, 41051125, 1521641624], 'label': '46656.ir.36.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dm1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714650
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ba1', '972.q1', '972.bs1', '1458.f1', '1458.h1', '1458.j1'], 'contains': ['5832.d1', '5832.f1', '5832.n1', '5832.bg1', '5832.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 41051299, 39957564, 39916800], 'label': '46656.ir.2916.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714651
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bb1', '324.cl1', '972.r1', '1458.e1', '1458.h1', '1458.k1'], 'contains': ['5832.n1', '5832.bj1', '5832.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 1174320, 6227827818, 40320], 'label': '46656.ir.2916.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '2916.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714652
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bc1', '324.cm1', '972.s1', '1458.f1', '1458.g1', '1458.k1'], 'contains': ['5832.n1', '5832.bl1', '5832.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 1174320, 6267381738, 40320], 'label': '46656.ir.2916.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714653
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cn1', '972.v1', '972.w1', '972.x1', '1458.i1'], 'contains': ['5832.o1', '5832.q1', '5832.s1', '5832.bu1', '5832.bw1', '5832.cc1', '5832.ch1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 1174320, 40320, 39957127], 'label': '46656.ir.2916.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714654
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.co1', '972.y1', '972.z1', '1458.i1'], 'contains': ['5832.p1', '5832.q1', '5832.r1', '5832.bz1', '5832.cb1', '5832.cd1', '5832.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [1174320, 40320, 6227827207, 39957127], 'label': '46656.ir.2916.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714655
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.bd1', '972.bj1', '972.bt1', '1458.i1', '1458.j1', '1458.k1'], 'contains': ['5832.b1', '5832.i1', '5832.n1', '5832.q1', '5832.t1', '5832.bo1', '5832.cj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41050800, 7, 39916800], 'label': '46656.ir.2916.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '2916.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714656
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cq1', '972.bk1', '972.bm1', '972.bu1', '1458.i1'], 'contains': ['5832.h1', '5832.k1', '5832.o1', '5832.p1', '5832.t1', '5832.bx1', '5832.ci1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 39916800, 6227827200], 'label': '46656.ir.2916.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '2916.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714657
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.cr1', '972.bn1', '972.bo1', '972.bp1', '972.bv1', '1458.i1'], 'contains': ['5832.j1', '5832.l1', '5832.r1', '5832.s1', '5832.t1', '5832.ck1', '5832.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 41050800, 39916800, 6227827207], 'label': '46656.ir.2916.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714658
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ee1', '972.bw1', '972.by1', '972.bz1', '972.cg1', '972.ch1', '1458.a1'], 'contains': ['5832.u1', '5832.v1', '5832.y1', '5832.ba1', '5832.bc1', '5832.bp1', '5832.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [180790853484, 41091120, 499, 444], 'label': '46656.ir.2916.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '2916.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714659
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ef1', '972.bx1', '972.ca1', '972.ci1', '1458.a1'], 'contains': ['5832.u1', '5832.w1', '5832.x1', '5832.bb1', '5832.bc1', '5832.bq1', '5832.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [180790853484, 41091120, 41051299, 444], 'label': '46656.ir.2916.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '2916.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714660
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '12.j1', '12.k1', '12.r1', '12.s1', '12.by1', '12.bz1', '18.l1', '54.s1', '54.ba1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 7, 41051125, 6227827818, 269279866800, 1521641624], 'label': '46656.ir.6.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714661
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1', '18.j1'], 'contains': ['72.gb1', '72.gd1', '72.gh1', '72.gv1', '72.gz1', '72.hg1', '72.hi1', '108.fi1', '324.fc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 41051125, 1481684400, 6227827200, 1521641624], 'label': '46656.ir.36.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dn1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714662
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.eg1', '972.cb1', '972.cj1', '1458.a1', '1458.e1', '1458.l1'], 'contains': ['5832.v1', '5832.x1', '5832.z1', '5832.be1', '5832.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [499, 443130957804, 444, 2957880240], 'label': '46656.ir.2916.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '2916.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714663
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.eh1', '972.cd1', '972.ck1', '1458.a1', '1458.f1', '1458.m1'], 'contains': ['5832.w1', '5832.y1', '5832.z1', '5832.bg1', '5832.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [40819, 443130957804, 444, 2957880240], 'label': '46656.ir.2916.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714664
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.de1', '324.ei1', '972.cc1', '1458.b1', '1458.e1', '1458.m1'], 'contains': ['5832.z1', '5832.bh1', '5832.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39917299, 443130957804, 444, 2957880240], 'label': '46656.ir.2916.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '2916.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714665
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.df1', '324.ej1', '972.ce1', '1458.b1', '1458.f1', '1458.l1'], 'contains': ['5832.z1', '5832.bk1', '5832.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [443130957804, 444, 39957619, 2957880240], 'label': '46656.ir.2916.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714666
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dg1', '972.cf1', '972.cl1', '972.dk1', '1458.i1', '1458.l1', '1458.m1'], 'contains': ['5832.z1', '5832.bi1', '5832.bo1', '5832.bw1', '5832.bx1', '5832.cg1', '5832.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 41050800, 7, 6227827207], 'label': '46656.ir.2916.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714667
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.el1', '972.cm1', '972.cy1', '1458.a1', '1458.g1', '1458.n1'], 'contains': ['5832.bd1', '5832.be1', '5832.bl1', '5832.bp1', '5832.bs1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 137, 7, 1174320], 'label': '46656.ir.2916.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714668
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.em1', '972.co1', '972.cz1', '1458.a1', '1458.h1', '1458.o1'], 'contains': ['5832.bd1', '5832.bg1', '5832.bj1', '5832.bq1', '5832.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 6227827342, 7, 1174320], 'label': '46656.ir.2916.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714669
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dl1', '324.en1', '972.cn1', '1458.b1', '1458.g1', '1458.o1'], 'contains': ['5832.bd1', '5832.bh1', '5832.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 7, 1174320, 6267381262], 'label': '46656.ir.2916.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714670
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dm1', '324.eo1', '972.cp1', '1458.b1', '1458.h1', '1458.n1'], 'contains': ['5832.bd1', '5832.bk1', '5832.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 39957257, 7, 1174320], 'label': '46656.ir.2916.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714671
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dn1', '324.ep1', '972.cq1', '1458.c1', '1458.e1', '1458.n1'], 'contains': ['5832.be1', '5832.bf1', '5832.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [137, 7, 1174320, 6227464327], 'label': '46656.ir.2916.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '2916.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714672
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.ca1', '12.cb1', '18.p1'], 'contains': ['72.ga1', '72.gc1', '72.gi1', '72.gt1', '72.gx1', '72.hl1', '72.hp1', '108.fi1', '108.fj1', '324.fd1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 39366316080, 1521641955, 39957120, 41050800, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.36.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.do1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216714673
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.do1', '324.eq1', '972.cr1', '1458.c1', '1458.g1', '1458.l1'], 'contains': ['5832.be1', '5832.bi1', '5832.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [499, 444, 443609999724, 2957880240], 'label': '46656.ir.2916.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714674
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dp1', '324.er1', '972.ct1', '1458.c1', '1458.f1', '1458.o1'], 'contains': ['5832.bf1', '5832.bg1', '5832.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [7, 1174320, 6227464327, 6267381262], 'label': '46656.ir.2916.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714675
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dq1', '324.es1', '972.cs1', '1458.d1', '1458.e1', '1458.o1'], 'contains': ['5832.bf1', '5832.bh1', '5832.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6227827342, 7, 1174320, 6227464327], 'label': '46656.ir.2916.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '2916.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714676
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dr1', '324.et1', '972.cu1', '1458.d1', '1458.f1', '1458.n1'], 'contains': ['5832.bf1', '5832.bk1', '5832.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957257, 7, 1174320, 6227464327], 'label': '46656.ir.2916.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714677
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ds1', '324.eu1', '972.cw1', '1458.c1', '1458.h1', '1458.m1'], 'contains': ['5832.bg1', '5832.bi1', '5832.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [40819, 444, 443609999724, 2957880240], 'label': '46656.ir.2916.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714678
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dt1', '324.ev1', '972.cv1', '1458.d1', '1458.g1', '1458.m1'], 'contains': ['5832.bh1', '5832.bi1', '5832.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39917299, 444, 443609999724, 2957880240], 'label': '46656.ir.2916.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714679
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.du1', '324.ew1', '972.cx1', '1458.d1', '1458.h1', '1458.l1'], 'contains': ['5832.bi1', '5832.bj1', '5832.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [444, 443609999724, 39957619, 2957880240], 'label': '46656.ir.2916.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714680
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dv1', '972.da1', '972.df1', '972.dl1', '1458.i1', '1458.n1', '1458.o1'], 'contains': ['5832.bd1', '5832.bf1', '5832.bo1', '5832.cb1', '5832.ch1', '5832.ci1', '5832.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800, 7], 'label': '46656.ir.2916.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714681
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ey1', '972.db1', '972.dg1', '1458.j1', '1458.l1', '1458.n1'], 'contains': ['5832.be1', '5832.bk1', '5832.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41050800, 499, 39957564], 'label': '46656.ir.2916.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '2916.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714682
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ez1', '972.dc1', '972.dh1', '1458.j1', '1458.m1', '1458.o1'], 'contains': ['5832.bg1', '5832.bh1', '5832.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39917299, 39957120, 41050800, 39957564], 'label': '46656.ir.2916.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '2916.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714683
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1', '18.m1'], 'contains': ['72.b1', '72.hk1', '72.hq1', '108.fj1', '144.ev1', '972.do1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827200, 623823424560], 'label': '46656.ir.36.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dp1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714684
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dy1', '324.fa1', '972.dd1', '972.di1', '1458.k1', '1458.l1', '1458.o1'], 'contains': ['5832.bj1', '5832.bn1', '5832.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 39957120, 41050800, 6227827818], 'label': '46656.ir.2916.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.br1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714685
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.dz1', '324.fb1', '972.de1', '972.dj1', '1458.k1', '1458.m1', '1458.n1'], 'contains': ['5832.bl1', '5832.bm1', '5832.bo1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 39957120, 41050800, 6267744618], 'label': '46656.ir.2916.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714686
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ff1', '972.dm1', '972.dn1', '972.do1', '1458.i1'], 'contains': ['5832.bu1', '5832.bv1', '5832.bx1', '5832.cd1', '5832.cf1', '5832.cj1', '5832.cl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 6227827200], 'label': '46656.ir.2916.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714687
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2916.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.fj1', '972.dp1', '972.dq1', '972.dr1', '1458.i1'], 'contains': ['5832.bz1', '5832.ca1', '5832.cc1', '5832.ce1', '5832.ci1', '5832.cj1', '5832.ck1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 6227827207], 'label': '46656.ir.2916.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '2916.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714688
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.b1', '1296.c1', '1296.bo1', '1944.c1', '1944.e1', '1944.f1', '1944.g1', '1944.h1', '1944.ba1', '1944.cf1'], 'contains': ['7776.b1', '7776.g1', '7776.bm1', '11664.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [7, 39916800, 37885034880], 'label': '46656.ir.3888.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714689
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.b1', '1296.d1', '1296.bn1', '1944.a1', '1944.b1', '1944.d1', '1944.i1', '1944.j1', '1944.k1', '1944.l1'], 'contains': ['7776.c1', '7776.i1', '7776.bn1', '11664.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 7, 39916800], 'label': '46656.ir.3888.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '3888.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714690
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.c1', '1296.d1', '1296.e1', '1296.bp1', '1944.m1', '1944.n1', '1944.bb1'], 'contains': ['7776.a1', '7776.k1', '7776.bo1', '11664.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [7, 39916800, 435], 'label': '46656.ir.3888.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '3888.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714691
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.f1', '1296.g1', '1296.h1', '1296.i1', '1296.bq1', '1944.m1', '1944.o1', '1944.r1'], 'contains': ['7776.a1', '7776.l1', '7776.bf1', '11664.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916800, 6227827200, 435], 'label': '46656.ir.3888.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '3888.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714692
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.f1', '1296.j1', '1296.br1', '1944.a1', '1944.p1', '1944.t1'], 'contains': ['7776.c1', '7776.o1', '7776.bg1', '11664.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 39916800, 6227827200], 'label': '46656.ir.3888.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '3888.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714693
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.f1', '1296.g1', '1296.k1', '1296.bs1', '1944.q1'], 'contains': ['7776.e1', '7776.r1', '7776.bh1', '11664.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316184, 39916800, 6227827200], 'label': '46656.ir.3888.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.p1', 'old_label': '3888.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714694
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1', '18.j1'], 'contains': ['72.gl1', '72.gm1', '72.gu1', '72.gy1', '72.hf1', '72.hg1', '72.hh1', '108.fm1', '324.fg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 41051125, 1481684400, 6227827207, 1521641624], 'label': '46656.ir.36.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dq1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216714695
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.i1', '1296.j1', '1296.k1', '1296.bt1', '1944.b1', '1944.s1', '1944.t1'], 'contains': ['7776.c1', '7776.s1', '7776.bk1', '11664.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916800, 40323593520, 6227827200], 'label': '46656.ir.3888.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '3888.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714696
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bv1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.l1', '1296.m1', '1296.n1', '1296.bu1', '1944.n1', '1944.r1', '1944.u1', '1944.v1', '1944.w1', '1944.x1', '1944.bx1'], 'contains': ['7776.a1', '7776.u1', '7776.ba1', '11664.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957120, 39957224, 1134000], 'label': '46656.ir.3888.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '3888.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714697
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.m1', '1296.o1', '1296.bw1', '1944.c1', '1944.y1', '1944.ch1'], 'contains': ['7776.b1', '7776.x1', '7776.bd1', '11664.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 1134000, 37885034880], 'label': '46656.ir.3888.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '3888.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714698
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.n1', '1296.o1', '1296.bv1', '1944.d1', '1944.t1', '1944.z1'], 'contains': ['7776.c1', '7776.z1', '7776.be1', '11664.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 39957120, 1134000], 'label': '46656.ir.3888.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '3888.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714699
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.p1', '1296.q1', '1296.r1', '1296.bx1', '1944.y1', '1944.ba1', '1944.cg1'], 'contains': ['7776.b1', '7776.bm1', '7776.bz1', '11664.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1481684400, 39916800, 39957127], 'label': '46656.ir.3888.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '3888.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714700
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.p1', '1296.s1', '1296.t1', '1296.u1', '1296.by1', '1944.u1', '1944.bb1', '1944.bh1'], 'contains': ['7776.a1', '7776.bo1', '7776.ca1', '11664.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [40320, 39957127, 104], 'label': '46656.ir.3888.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.ce1', 'old_label': '3888.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714701
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.r1', '1296.s1', '1296.ca1', '1944.y1', '1944.bi1', '1944.cf1'], 'contains': ['7776.b1', '7776.bp1', '7776.cb1', '11664.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916800, 39957127, 37885034880], 'label': '46656.ir.3888.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714702
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.q1', '1296.s1', '1296.t1', '1296.bz1', '1944.bj1'], 'contains': ['7776.d1', '7776.bq1', '7776.cd1', '11664.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [268280813235, 40320, 39957127], 'label': '46656.ir.3888.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '3888.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714703
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.v1', '1296.w1', '1296.x1', '1296.cb1', '1944.a1', '1944.s1', '1944.z1'], 'contains': ['7776.c1', '7776.bt1', '7776.cn1', '11664.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39366316080, 39916800, 6227827207], 'label': '46656.ir.3888.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714704
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.v1', '1296.y1', '1296.z1', '1296.ba1', '1296.cc1', '1944.m1', '1944.o1', '1944.v1'], 'contains': ['7776.a1', '7776.bu1', '7776.co1', '11664.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916800, 6227827207, 435], 'label': '46656.ir.3888.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '3888.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714705
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.cc1', '12.cd1', '18.p1'], 'contains': ['72.go1', '72.gp1', '72.gs1', '72.gw1', '72.hj1', '72.hl1', '72.hm1', '108.fm1', '108.fn1', '324.fi1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207, 1521641624], 'label': '46656.ir.36.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '36.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dr1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216714706
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.w1', '1296.y1', '1296.cd1', '1944.b1', '1944.p1', '1944.z1'], 'contains': ['7776.c1', '7776.bv1', '7776.cr1', '11664.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916800, 40323593520, 6227827207], 'label': '46656.ir.3888.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '3888.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714707
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.x1', '1296.y1', '1296.z1', '1296.ce1', '1944.q1'], 'contains': ['7776.e1', '7776.bw1', '7776.cu1', '11664.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 39916800, 6227827207], 'label': '46656.ir.3888.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '3888.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714708
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.bb1', '1296.bc1', '1296.bd1', '1296.be1', '1296.bf1', '1296.cf1', '1944.n1', '1944.o1', '1944.bh1'], 'contains': ['7776.a1', '7776.ca1', '7776.cg1', '11664.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [1134000, 39957127, 435], 'label': '46656.ir.3888.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '3888.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714709
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bb1', '1296.bg1', '1296.bh1', '1296.cj1', '1944.c1', '1944.bi1', '1944.cg1'], 'contains': ['7776.b1', '7776.cb1', '7776.ch1', '11664.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1134000, 39957127, 37885034880], 'label': '46656.ir.3888.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '3888.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714710
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bc1', '1296.bh1', '1296.bi1', '1296.cg1', '1944.d1', '1944.p1', '1944.s1'], 'contains': ['7776.c1', '7776.cc1', '7776.cj1', '11664.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [387037284480, 1134000, 39957127], 'label': '46656.ir.3888.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714711
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.bb1', '1296.bd1', '1296.bg1', '1296.bi1', '1296.bj1', '1296.bj2', '1296.ch1', '1944.bj1'], 'contains': ['7776.d1', '7776.cd1', '7776.ck1', '11664.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [37885034984, 1134000, 39957127], 'label': '46656.ir.3888.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.bj1', 'old_label': '3888.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714712
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.bc1', '1296.be1', '1296.bg1', '1296.bi1', '1296.bj1', '1296.bj2', '1296.ci1', '1944.q1'], 'contains': ['7776.e1', '7776.ce1', '7776.cm1', '11664.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [293708218035, 1134000, 39957127], 'label': '46656.ir.3888.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.q1', 'old_label': '3888.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714713
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.cz1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.bk1', '1296.bl1', '1296.bm1', '1296.ck1', '1944.bb1', '1944.bc1', '1944.bf1', '1944.bh1', '1944.bl1', '1944.bm1', '1944.bx1'], 'contains': ['7776.a1', '7776.ba1', '11664.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 39957224, 39916800], 'label': '46656.ir.3888.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '3888.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714714
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bk1', '1296.cm1', '1944.ba1', '1944.bd1', '1944.bg1', '1944.bi1', '1944.bk1', '1944.bn1', '1944.ch1'], 'contains': ['7776.b1', '7776.bb1', '11664.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 1481684400, 39916800], 'label': '46656.ir.3888.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714715
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.bk1', '1296.bl1', '1296.cl1', '1944.be1', '1944.bj1', '1944.bo1'], 'contains': ['7776.d1', '7776.bc1', '11664.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1521641955, 39957120, 39916800], 'label': '46656.ir.3888.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '3888.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714716
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '36.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1', '18.m1'], 'contains': ['72.c1', '72.hk1', '72.hn1', '108.fn1', '144.hm1', '972.dq1'], 'core': '72.c1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207, 623823424560], 'label': '46656.ir.36.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ds1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216714717
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bn1', '1296.bo1', '1296.bp1', '1944.bp1', '1944.bq1', '1944.br1', '1944.bs1', '1944.bt1', '1944.bu1', '1944.cf1'], 'contains': ['7776.f1', '7776.g1', '7776.bp1', '11664.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 39916800], 'label': '46656.ir.3888.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '3888.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714718
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.ef1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bq1', '1296.br1', '1296.bs1', '1296.bt1', '1944.bp1', '1944.bv1', '1944.bw1'], 'contains': ['7776.f1', '7776.m1', '7776.bi1', '11664.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 39916800, 6227827200], 'label': '46656.ir.3888.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '3888.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714719
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bu1', '1296.bv1', '1296.bw1', '1944.bq1', '1944.bw1', '1944.ca1', '1944.cb1', '1944.cc1', '1944.cd1', '1944.ch1'], 'contains': ['7776.f1', '7776.x1', '7776.bb1', '11664.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 1481684400, 1134000], 'label': '46656.ir.3888.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714720
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bx1', '1296.by1', '1296.bz1', '1296.ca1', '1944.ca1', '1944.cf1', '1944.cg1'], 'contains': ['7776.f1', '7776.bm1', '7776.cb1', '11664.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 39916800, 39957127], 'label': '46656.ir.3888.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714721
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cb1', '1296.cc1', '1296.cd1', '1296.ce1', '1944.bp1', '1944.bv1', '1944.cb1'], 'contains': ['7776.f1', '7776.br1', '7776.cp1', '11664.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 39916800, 6227827207], 'label': '46656.ir.3888.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714722
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cf1', '1296.cg1', '1296.ch1', '1296.ci1', '1296.cj1', '1944.bq1', '1944.bv1', '1944.ce1', '1944.cg1'], 'contains': ['7776.f1', '7776.bz1', '7776.ch1', '11664.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [1481684400, 1134000, 39957127], 'label': '46656.ir.3888.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714723
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ck1', '1296.cl1', '1296.cm1', '1296.cn1', '1944.cf1', '1944.cg1', '1944.ch1'], 'contains': ['7776.b1', '7776.f1', '7776.bd1', '11664.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 39916800, 37885034880], 'label': '46656.ir.3888.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '3888.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714724
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.co1', '1296.cp1', '1296.eg1', '1944.bp1', '1944.ci1', '1944.cl1', '1944.cm1', '1944.cn1', '1944.co1', '1944.cv1'], 'contains': ['7776.g1', '7776.m1', '7776.br1', '11664.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 7, 6227827207], 'label': '46656.ir.3888.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714725
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.co1', '1296.cr1', '1296.cs1', '1296.eh1', '1944.cj1', '1944.cp1', '1944.cq1'], 'contains': ['7776.h1', '7776.n1', '7776.bs1', '11664.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [387999647280, 7, 6227827207], 'label': '46656.ir.3888.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cs1', 'old_label': '3888.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714726
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.co1', '1296.cq1', '1296.ei1', '1944.a1', '1944.ck1', '1944.cr1', '1944.cs1', '1944.ct1', '1944.cu1', '1944.de1'], 'contains': ['7776.i1', '7776.o1', '7776.bt1', '11664.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 7, 6227827207], 'label': '46656.ir.3888.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714727
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '24.b1', '24.f1', '24.bb1', '24.bm1', '24.bn1'], 'contains': ['96.a1', '96.b1', '96.c1', '144.bs1', '144.cd1', '144.ce1', '144.cf1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.48.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': ['12.a1', '24.b1'], 'normal_contains': ['96.a1', '96.b1', '96.c1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216714728
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cp1', '1296.cq1', '1296.cr1', '1296.ej1', '1944.b1', '1944.cx1', '1944.cy1', '1944.cz1', '1944.da1', '1944.db1', '1944.de1'], 'contains': ['7776.i1', '7776.s1', '7776.bv1', '11664.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [7, 40323593520, 6227827207], 'label': '46656.ir.3888.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '3888.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714729
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.cl1', '1296.cs1', '1296.ek1', '1944.cw1', '1944.dc1', '1944.dd1'], 'contains': ['7776.j1', '7776.t1', '7776.bx1', '11664.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [624302466480, 7, 6227827207], 'label': '46656.ir.3888.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '3888.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714730
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.bd1', '1296.ct1', '1296.el1', '1944.cw1', '1944.df1', '1944.dg1'], 'contains': ['7776.j1', '7776.v1', '7776.cf1', '11664.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 7, 93576273840], 'label': '46656.ir.3888.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '3888.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714731
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cu1', '1296.cv1', '1296.em1', '1944.c1', '1944.bq1', '1944.ci1', '1944.dh1', '1944.di1', '1944.dj1', '1944.dk1'], 'contains': ['7776.g1', '7776.x1', '7776.ch1', '11664.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41091120, 7, 37885034880], 'label': '46656.ir.3888.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714732
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ct1', '1296.cu1', '1296.cw1', '1296.en1', '1944.cj1', '1944.dl1', '1944.dm1'], 'contains': ['7776.h1', '7776.y1', '7776.ci1', '11664.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 301891126320, 7], 'label': '46656.ir.3888.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '3888.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714733
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cu1', '1296.cv1', '1296.cw1', '1296.eo1', '1944.d1', '1944.ck1', '1944.cx1', '1944.dn1', '1944.do1', '1944.dp1', '1944.dq1'], 'contains': ['7776.i1', '7776.z1', '7776.cj1', '11664.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 39366316080, 7], 'label': '46656.ir.3888.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714734
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cx1', '1296.cy1', '1296.ep1', '1944.ba1', '1944.bq1', '1944.cv1', '1944.dr1', '1944.ds1', '1944.dt1', '1944.du1', '1944.dv1', '1944.dw1', '1944.dx1', '1944.dy1', '1944.dz1', '1944.ea1', '1944.eb1', '1944.em1'], 'contains': ['7776.g1', '7776.bb1', '7776.bz1', '11664.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 7, 1481684400], 'label': '46656.ir.3888.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714735
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cy1', '1296.cz1', '1296.eq1', '1944.c1', '1944.cf1', '1944.ed1', '1944.ee1', '1944.ef1', '1944.eg1', '1944.em1'], 'contains': ['7776.g1', '7776.bd1', '7776.cb1', '11664.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39957120, 7, 37885034880], 'label': '46656.ir.3888.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.br1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714736
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cx1', '1296.cz1', '1296.er1', '1944.d1', '1944.de1', '1944.ec1', '1944.eh1', '1944.ei1', '1944.ej1', '1944.ek1'], 'contains': ['7776.i1', '7776.be1', '7776.cc1', '11664.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [387037284480, 39957120, 7], 'label': '46656.ir.3888.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714737
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.da1', '1296.db1', '1296.dc1', '1296.es1', '1944.a1', '1944.cx1', '1944.ec1', '1944.en1', '1944.eo1', '1944.ep1', '1944.eq1'], 'contains': ['7776.i1', '7776.bg1', '7776.cn1', '11664.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 7], 'label': '46656.ir.3888.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714738
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1', 'complements': ['972.bm1', '972.bo1', '972.bp1', '972.dq1', '972.do1'], 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.b1', '24.g1', '24.bc1', '24.bp1', '24.bz1'], 'contains': ['96.a1', '144.cp1', '144.cx1', '144.df1', '432.cw1'], 'core': '48.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 499, 7, 325, 269279866800], 'label': '46656.ir.48.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': ['12.b1', '24.b1'], 'normal_contains': ['96.a1', '1296.a1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '46656.ir', 'quotient_action_image': '48.48', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '1728.47869'}
  • id: 216714739
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.da1', '1296.dd1', '1296.et1', '1944.bp1', '1944.ci1', '1944.dr1', '1944.er1', '1944.es1', '1944.et1', '1944.eu1'], 'contains': ['7776.g1', '7776.bi1', '7776.cp1', '11664.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 268280812800, 7], 'label': '46656.ir.3888.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714740
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.dc1', '1296.dd1', '1296.de1', '1296.df1', '1296.eu1', '1944.cj1', '1944.ev1', '1944.ew1'], 'contains': ['7776.h1', '7776.bj1', '7776.cq1', '11664.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 301891126320, 7], 'label': '46656.ir.3888.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '3888.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714741
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.db1', '1296.dd1', '1296.ev1', '1944.b1', '1944.ck1', '1944.ec1', '1944.ex1', '1944.ey1', '1944.ez1', '1944.fa1'], 'contains': ['7776.i1', '7776.bk1', '7776.cr1', '11664.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 7, 40323593520], 'label': '46656.ir.3888.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '3888.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714742
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.da1', '1296.de1', '1296.ew1', '1944.cw1', '1944.fb1', '1944.fc1'], 'contains': ['7776.j1', '7776.bl1', '7776.cv1', '11664.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 7, 655477406640], 'label': '46656.ir.3888.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '3888.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714743
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.er1', '1296.dg1', '1296.do1', '1944.e1', '1944.br1', '1944.cl1', '1944.dh1', '1944.ds1', '1944.ed1', '1944.er1'], 'contains': ['7776.g1', '11664.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [31658054844, 499, 37885034880], 'label': '46656.ir.3888.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '3888.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.by1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714744
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.es1', '1296.dp1', '1296.dq1', '1944.e1', '1944.f1', '1944.bs1', '1944.di1', '1944.du1', '1944.ee1', '1944.ef1'], 'contains': ['7776.g1', '11664.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 39917299, 37885034880], 'label': '46656.ir.3888.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714745
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.et1', '1296.dh1', '1296.dq1', '1944.g1', '1944.br1', '1944.cm1', '1944.dj1', '1944.dv1', '1944.ef1', '1944.es1'], 'contains': ['7776.g1', '11664.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 268280812800, 355419187644], 'label': '46656.ir.3888.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '3888.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ca1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714746
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.eu1', '1296.di1', '1296.dj1', '1944.bt1', '1944.cl1', '1944.cn1', '1944.dk1', '1944.dx1', '1944.es1', '1944.et1'], 'contains': ['7776.g1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 268280812800, 6227827818], 'label': '46656.ir.3888.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714747
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ev1', '1296.dk1', '1296.ds1', '1944.h1', '1944.bu1', '1944.co1', '1944.dh1', '1944.dv1', '1944.ee1', '1944.et1'], 'contains': ['7776.g1', '11664.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [31658054844, 41091619, 37885034880], 'label': '46656.ir.3888.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714748
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ew1', '1296.dl1', '1296.dt1', '1944.f1', '1944.bu1', '1944.cn1', '1944.dj1', '1944.ds1', '1944.eg1', '1944.eu1'], 'contains': ['7776.g1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [1481684400, 39957619, 1481684844], 'label': '46656.ir.3888.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714749
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['972.bm1', '972.dq1', '972.bo1', '972.bp1', '972.do1'], 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '24.b1', '24.j1', '24.bf1', '24.br1', '24.cb1'], 'contains': ['96.a1', '144.ct1', '144.db1', '144.dh1', '432.cz1'], 'core': '48.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 7, 41091619, 325, 269279866800], 'label': '46656.ir.48.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': ['12.c1', '24.b1'], 'normal_contains': ['96.a1'], 'normalizer': '1.a1', 'old_label': '48.c1', 'projective_image': '46656.ir', 'quotient_action_image': '48.48', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216714750
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ex1', '1296.dt1', '1296.du1', '1944.g1', '1944.h1', '1944.bs1', '1944.di1', '1944.dy1', '1944.ed1', '1944.eg1'], 'contains': ['7776.g1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [31658054844, 39957619, 37885034880], 'label': '46656.ir.3888.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ce1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714751
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ey1', '1296.dm1', '1296.dn1', '1944.bt1', '1944.cm1', '1944.co1', '1944.dk1', '1944.dz1', '1944.er1', '1944.eu1'], 'contains': ['7776.g1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 268280812800, 6267744618], 'label': '46656.ir.3888.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714752
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ez1', '1296.dg1', '1296.dw1', '1296.ea1', '1296.ee1', '1944.cp1', '1944.dl1', '1944.ev1'], 'contains': ['7776.h1', '11664.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [301891126320, 499, 444], 'label': '46656.ir.3888.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '3888.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714753
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fa1', '1296.di1', '1296.dx1', '1296.eb1', '1944.cp1', '1944.dm1', '1944.ew1'], 'contains': ['7776.h1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [469, 387999647280, 6227827818], 'label': '46656.ir.3888.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cs1', 'old_label': '3888.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ch1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714754
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fb1', '1296.dk1', '1296.dy1', '1296.ec1', '1944.cq1', '1944.dl1', '1944.ew1'], 'contains': ['7776.h1', '11664.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091619, 301891126320, 444], 'label': '46656.ir.3888.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '3888.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714755
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fc1', '1296.dn1', '1296.dz1', '1296.ed1', '1296.ef1', '1944.cq1', '1944.dm1', '1944.ev1'], 'contains': ['7776.h1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [469, 301891126320, 6267744618], 'label': '46656.ir.3888.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '3888.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714756
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fd1', '1296.dg1', '1296.do1', '1296.dw1', '1944.i1', '1944.cr1', '1944.cy1', '1944.dn1', '1944.eh1', '1944.en1', '1944.ex1'], 'contains': ['7776.i1', '11664.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 499, 444], 'label': '46656.ir.3888.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '3888.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ck1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714757
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fe1', '1296.dh1', '1296.dp1', '1944.i1', '1944.cs1', '1944.cz1', '1944.do1', '1944.ei1', '1944.eo1', '1944.ey1'], 'contains': ['7776.i1', '11664.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39917299, 39366316080, 444], 'label': '46656.ir.3888.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '3888.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714758
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ff1', '1296.di1', '1296.dr1', '1944.j1', '1944.cr1', '1944.da1', '1944.dp1', '1944.ej1', '1944.eo1', '1944.ez1'], 'contains': ['7776.i1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 39366316080, 6227827818], 'label': '46656.ir.3888.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714759
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fg1', '1296.dj1', '1296.dr1', '1296.dx1', '1944.k1', '1944.ct1', '1944.cy1', '1944.dq1', '1944.ej1', '1944.ep1', '1944.ey1'], 'contains': ['7776.i1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 6227827818, 40323593520], 'label': '46656.ir.3888.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '3888.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714760
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['972.cg1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.c1', '24.d1', '24.ck1', '24.cw1', '24.db1', '24.de1'], 'contains': ['96.o1', '144.gr1', '144.gs1'], 'core': '48.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.48.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': ['16.a1', '24.a1', '24.c1', '24.d1'], 'normal_contains': ['192.a1', '432.a1'], 'normalizer': '1.a1', 'old_label': '48.d1', 'projective_image': '46656.ir', 'quotient_action_image': '48.35', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216714761
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fh1', '1296.dk1', '1296.ds1', '1296.dy1', '1944.l1', '1944.cu1', '1944.db1', '1944.dn1', '1944.ei1', '1944.ep1', '1944.ez1'], 'contains': ['7776.i1', '11664.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091619, 39366316080, 444], 'label': '46656.ir.3888.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.co1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714762
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fi1', '1296.dl1', '1296.du1', '1944.l1', '1944.ct1', '1944.da1', '1944.do1', '1944.eh1', '1944.eq1', '1944.fa1'], 'contains': ['7776.i1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [387037284480, 444, 39957619], 'label': '46656.ir.3888.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714763
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fj1', '1296.dm1', '1296.dv1', '1296.dz1', '1944.j1', '1944.cs1', '1944.db1', '1944.dq1', '1944.ek1', '1944.en1', '1944.fa1'], 'contains': ['7776.i1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [469, 39366316080, 6267744618], 'label': '46656.ir.3888.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714764
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fk1', '1296.dn1', '1296.dv1', '1944.k1', '1944.cu1', '1944.cz1', '1944.dp1', '1944.ek1', '1944.eq1', '1944.ex1'], 'contains': ['7776.i1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 6267744618, 40323593520], 'label': '46656.ir.3888.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '3888.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714765
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.eo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fl1', '972.db1', '1296.ea1', '1944.dc1', '1944.df1', '1944.fb1'], 'contains': ['7776.j1', '11664.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [499, 655477406640, 444], 'label': '46656.ir.3888.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '3888.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714766
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fm1', '972.dd1', '1296.eb1', '1944.dc1', '1944.dg1', '1944.fc1'], 'contains': ['7776.j1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [469, 624302466480, 6227827818], 'label': '46656.ir.3888.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '3888.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ct1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714767
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fn1', '972.dc1', '1296.ec1', '1944.dd1', '1944.df1', '1944.fc1'], 'contains': ['7776.j1', '11664.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091619, 93576273840, 444], 'label': '46656.ir.3888.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '3888.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714768
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.fo1', '972.de1', '1296.ed1', '1944.dd1', '1944.dg1', '1944.fb1'], 'contains': ['7776.j1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [469, 6267744618, 655477406640], 'label': '46656.ir.3888.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '3888.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714769
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.eg1', '1296.eh1', '1296.ei1', '1296.ej1', '1296.ek1', '1296.ex1', '1944.m1', '1944.fd1', '1944.fe1'], 'contains': ['7776.k1', '7776.l1', '7776.bu1', '11664.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [7, 6227827207, 104], 'label': '46656.ir.3888.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '3888.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714770
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.el1', '1296.em1', '1296.en1', '1296.eo1', '1296.ey1', '1944.n1', '1944.fd1'], 'contains': ['7776.k1', '7776.u1', '7776.cg1', '11664.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091120, 7, 435], 'label': '46656.ir.3888.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '3888.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714771
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.b1', '12.bf1', '12.bi1', '12.bj1', '12.bq1', '12.bw1', '12.by1', '18.u1', '54.bb1', '54.bf1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 499, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.6.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714772
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.f1', '24.g1', '24.h1', '24.i1', '24.j1', '24.r1'], 'contains': ['96.a1', '96.d1', '96.t1', '144.b1', '144.h1', '144.i1', '144.j1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 7, 325, 269279866800], 'label': '46656.ir.48.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '1728.47045'}
  • id: 216714773
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ep1', '1296.eq1', '1296.er1', '1296.ez1', '1944.n1', '1944.bb1', '1944.fe1', '1944.ff1', '1944.fg1', '1944.fh1', '1944.fi1'], 'contains': ['7776.k1', '7776.ba1', '7776.ca1', '11664.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957555, 39957120, 7], 'label': '46656.ir.3888.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '3888.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714774
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.es1', '1296.et1', '1296.eu1', '1296.ev1', '1296.ew1', '1296.fa1', '1944.m1', '1944.fd1', '1944.ff1'], 'contains': ['7776.k1', '7776.bf1', '7776.co1', '11664.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 7, 104], 'label': '46656.ir.3888.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '3888.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714775
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fg1', '1296.fh1', '1296.fi1', '1296.fj1', '1296.gm1', '1296.gn1', '1944.r1', '1944.fd1', '1944.fj1'], 'contains': ['7776.l1', '7776.u1', '7776.bf1', '11664.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [41091120, 6227827200, 104], 'label': '46656.ir.3888.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.l1', 'old_label': '3888.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.da1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714776
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.eg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fh1', '1296.fk1', '1296.gp1', '1944.bw1', '1944.ci1', '1944.fl1'], 'contains': ['7776.m1', '7776.x1', '7776.bi1', '11664.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 268280812800, 6227827200], 'label': '46656.ir.3888.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '3888.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.db1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714777
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ha1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fi1', '1296.fk1', '1296.go1', '1296.gr1', '1944.cj1'], 'contains': ['7776.n1', '7776.y1', '7776.bj1', '11664.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 387999647280, 6227827200], 'label': '46656.ir.3888.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '3888.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714778
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fj1', '1296.fk1', '1296.gq1', '1944.t1', '1944.ck1', '1944.fk1'], 'contains': ['7776.o1', '7776.z1', '7776.bk1', '11664.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 6227827200], 'label': '46656.ir.3888.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '3888.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714779
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fl1', '1296.fm1', '1296.fn1', '1296.gs1', '1944.a1', '1944.fk1', '1944.fx1'], 'contains': ['7776.o1', '7776.bn1', '7776.cn1', '11664.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916807, 39366316080, 6227827200], 'label': '46656.ir.3888.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.de1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714780
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fl1', '1296.fo1', '1296.fp1', '1296.fq1', '1296.gt1', '1944.m1', '1944.fj1', '1944.fn1'], 'contains': ['7776.l1', '7776.bo1', '7776.co1', '11664.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 6227827200, 104], 'label': '46656.ir.3888.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '3888.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.df1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714781
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fm1', '1296.fo1', '1296.gu1', '1944.bp1', '1944.fl1', '1944.fo1'], 'contains': ['7776.m1', '7776.bp1', '7776.cp1', '11664.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 268280812800, 6227827200], 'label': '46656.ir.3888.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714782
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fn1', '1296.fo1', '1296.fp1', '1296.gv1', '1944.fp1'], 'contains': ['7776.p1', '7776.bq1', '7776.cs1', '11664.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [39916807, 268280813235, 6227827200], 'label': '46656.ir.3888.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '3888.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714783
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.k1', '24.l1'], 'contains': ['96.d1', '96.h1', '96.p1', '144.c1', '144.k1', '144.l1', '144.m1', '144.n1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 39916800, 269279866800, 6227827200], 'label': '46656.ir.48.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '288.950'}
  • id: 216714784
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fr1', '1296.fs1', '1296.ft1', '1296.gw1', '1944.bv1', '1944.cv1', '1944.fl1'], 'contains': ['7776.m1', '7776.br1', '7776.bz1', '11664.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1174327, 268280812800, 6227827207], 'label': '46656.ir.3888.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '3888.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.di1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714785
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fr1', '1296.fu1', '1296.fv1', '1296.fw1', '1296.gx1', '1944.o1', '1944.fe1', '1944.fj1'], 'contains': ['7776.l1', '7776.bu1', '7776.ca1', '11664.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1174327, 6227827207, 435], 'label': '46656.ir.3888.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.br1', 'old_label': '3888.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714786
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fs1', '1296.fu1', '1296.gy1', '1944.p1', '1944.de1', '1944.fk1'], 'contains': ['7776.o1', '7776.bv1', '7776.cc1', '11664.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 40323593520, 6227827207], 'label': '46656.ir.3888.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714787
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ft1', '1296.fu1', '1296.fv1', '1296.gz1', '1944.q1'], 'contains': ['7776.r1', '7776.bw1', '7776.ce1', '11664.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 1174327, 6227827207], 'label': '46656.ir.3888.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '3888.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714788
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fx1', '1296.fy1', '1296.fz1', '1296.ga1', '1296.gb1', '1296.gc1', '1296.gd1', '1296.ha1', '1296.hd1', '1944.o1', '1944.fd1', '1944.fn1'], 'contains': ['7776.l1', '7776.cg1', '7776.co1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [6227827200, 104, 41091127], 'label': '46656.ir.3888.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.j1', 'old_label': '3888.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714789
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fx1', '1296.ge1', '1296.gf1', '1296.he1', '1944.bv1', '1944.ci1', '1944.fo1'], 'contains': ['7776.m1', '7776.ch1', '7776.cp1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [268280812800, 6227827200, 41091127], 'label': '46656.ir.3888.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '3888.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714790
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fy1', '1296.ge1', '1296.gg1', '1296.hb1', '1296.hg1', '1944.cj1'], 'contains': ['7776.n1', '7776.ci1', '7776.cq1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [387999647280, 6227827200, 41091127], 'label': '46656.ir.3888.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '3888.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.do1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714791
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fz1', '1296.ge1', '1296.gh1', '1296.hf1', '1944.p1', '1944.ck1', '1944.fx1'], 'contains': ['7776.o1', '7776.cj1', '7776.cr1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39366316080, 6227827200, 41091127], 'label': '46656.ir.3888.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714792
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fx1', '1296.ga1', '1296.gg1', '1296.gh1', '1296.gi1', '1296.gi2', '1296.hh1', '1944.fp1'], 'contains': ['7776.p1', '7776.ck1', '7776.cs1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [268280813235, 6227827200, 41091127], 'label': '46656.ir.3888.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.fp1', 'old_label': '3888.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714793
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fy1', '1296.gb1', '1296.gf1', '1296.gg1', '1296.gh1', '1296.gi1', '1296.gi2', '1296.hc1', '1296.hj1'], 'contains': ['7776.q1', '7776.cl1', '7776.ct1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': None, 'generators': [295664181224, 6227827200, 41091127], 'label': '46656.ir.3888.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3888.dr1', 'old_label': '3888.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714794
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.f1', '24.l1', '24.m1', '24.n1', '24.o1', '24.p1'], 'contains': ['96.b1', '96.d1', '96.o1', '144.d1', '144.o1', '144.p1', '144.q1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 325, 1481684400, 269279866800, 1134000, 1521641624], 'label': '46656.ir.48.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216714795
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.fz1', '1296.gc1', '1296.gf1', '1296.gg1', '1296.gi1', '1296.gi2', '1296.hi1', '1944.q1'], 'contains': ['7776.r1', '7776.cm1', '7776.cu1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [39366316515, 6227827200, 41091127], 'label': '46656.ir.3888.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.q1', 'old_label': '3888.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ds1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714796
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.ca1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.gj1', '1296.gk1', '1296.gl1', '1296.hk1', '1944.r1', '1944.bc1', '1944.fe1', '1944.fn1', '1944.fq1', '1944.fr1', '1944.fu1'], 'contains': ['7776.l1', '7776.ba1', '11664.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1174320, 6227827200, 104], 'label': '46656.ir.3888.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '3888.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714797
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.dx1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.gj1', '1296.hl1', '1944.bd1', '1944.bw1', '1944.cv1', '1944.fm1', '1944.fo1', '1944.fs1', '1944.fv1'], 'contains': ['7776.m1', '7776.bb1', '11664.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 6227827200], 'label': '46656.ir.3888.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.du1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714798
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.gi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.gj1', '1296.gk1', '1296.hm1', '1944.be1', '1944.fp1', '1944.ft1'], 'contains': ['7776.p1', '7776.bc1', '11664.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1174320, 268280812904, 6227827200], 'label': '46656.ir.3888.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '3888.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714799
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.bm1', '1296.gm1', '1296.go1', '1944.cw1'], 'contains': ['7776.t1', '7776.v1', '7776.bl1', '11664.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 6227827200, 93575951280], 'label': '46656.ir.3888.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '3888.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714800
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.gn1', '1296.gp1', '1296.gq1', '1296.gr1', '1944.t1', '1944.cx1', '1944.fw1'], 'contains': ['7776.s1', '7776.z1', '7776.bg1', '11664.r1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 40323593520, 6227827200], 'label': '46656.ir.3888.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '3888.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714801
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.gs1', '1296.gt1', '1296.gu1', '1296.gv1', '1944.b1', '1944.fw1', '1944.fx1'], 'contains': ['7776.s1', '7776.bn1', '7776.cr1', '11664.s1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 40323593520, 6227827200], 'label': '46656.ir.3888.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '3888.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714802
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.gw1', '1296.gx1', '1296.gy1', '1296.gz1', '1944.s1', '1944.de1', '1944.fw1'], 'contains': ['7776.s1', '7776.bt1', '7776.cc1', '11664.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1174327, 39366316080, 6227827207], 'label': '46656.ir.3888.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.dz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714803
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.do1', '1296.ha1', '1296.hb1', '1296.hc1', '1944.cw1'], 'contains': ['7776.t1', '7776.cf1', '7776.cv1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6227827200, 93575951280, 41091127], 'label': '46656.ir.3888.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '3888.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ea1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714804
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hd1', '1296.he1', '1296.hf1', '1296.hg1', '1296.hh1', '1296.hi1', '1296.hj1', '1944.s1', '1944.cx1', '1944.fx1'], 'contains': ['7776.s1', '7776.cj1', '7776.cn1', '11664.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [40323593520, 6227827200, 41091127], 'label': '46656.ir.3888.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.eb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714805
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '24.r1', '24.u1'], 'contains': ['96.d1', '96.t1', '96.y1', '144.e1', '144.r1', '144.s1', '144.t1', '144.u1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 40320, 39957127], 'label': '46656.ir.48.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '48.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216714806
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hk1', '1296.hl1', '1296.hm1', '1296.hn1', '1944.t1', '1944.de1', '1944.fx1'], 'contains': ['7776.o1', '7776.s1', '7776.be1', '11664.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174320, 6227827200], 'label': '46656.ir.3888.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '3888.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ec1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714807
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ho1', '1296.hs1', '1296.ht1', '1296.hu1', '1944.n1', '1944.u1', '1944.fj1'], 'contains': ['7776.u1', '7776.bo1', '7776.ca1', '11664.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 39957127, 435], 'label': '46656.ir.3888.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '3888.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ed1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714808
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.hp1', '1296.hq1', '1296.hr1', '1296.hv1', '1296.hw1', '1296.hx1', '1296.ia1', '1944.v1', '1944.fd1', '1944.fj1'], 'contains': ['7776.u1', '7776.bu1', '7776.co1', '11664.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [41091120, 6227827207, 104], 'label': '46656.ir.3888.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.j1', 'old_label': '3888.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ee1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714809
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.bo1', '1296.hp1', '1296.hy1', '1944.cw1'], 'contains': ['7776.v1', '7776.bx1', '7776.cv1', '11664.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 6227827207, 93575951280], 'label': '46656.ir.3888.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '3888.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ef1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714810
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['972.bp1', '1296.hp1', '1296.hq1', '1296.hz1'], 'contains': ['7776.w1', '7776.by1', '7776.cw1', '11664.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': None, 'generators': [174452060544, 41091120, 6227827207], 'label': '46656.ir.3888.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3888.eg1', 'old_label': '3888.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.eg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714811
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hs1', '1296.ib1', '1296.id1', '1944.c1', '1944.y1', '1944.ca1'], 'contains': ['7776.x1', '7776.bm1', '7776.cb1', '11664.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 39957127, 37885034880], 'label': '46656.ir.3888.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '3888.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.eh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714812
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ht1', '1296.ib1', '1296.ic1', '1944.d1', '1944.fk1', '1944.fw1'], 'contains': ['7776.z1', '7776.bn1', '7776.cc1', '11664.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 387037284480, 39957127], 'label': '46656.ir.3888.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ei1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714813
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hu1', '1296.ic1', '1296.id1', '1944.y1', '1944.bq1', '1944.fl1', '1944.fz1'], 'contains': ['7776.x1', '7776.bp1', '7776.bz1', '11664.w1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41091120, 1481684400, 39957127], 'label': '46656.ir.3888.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ej1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714814
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hv1', '1296.ie1', '1296.if1', '1944.cb1', '1944.ci1', '1944.fl1'], 'contains': ['7776.x1', '7776.br1', '7776.cp1', '11664.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 268280812800, 6227827207], 'label': '46656.ir.3888.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '3888.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ek1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714815
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hw1', '1296.hy1', '1296.hz1', '1296.ie1', '1296.ih1', '1944.cj1'], 'contains': ['7776.y1', '7776.bs1', '7776.cq1', '11664.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41091120, 387999647280, 6227827207], 'label': '46656.ir.3888.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '3888.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.el1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714816
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.k1', '24.n1'], 'contains': ['96.d1', '96.w1', '96.bg1', '144.f1', '144.v1', '144.w1', '144.x1', '144.y1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 39916800, 269279866800, 6227827207], 'label': '46656.ir.48.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216714817
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.hx1', '1296.ie1', '1296.ig1', '1944.z1', '1944.ck1', '1944.fw1'], 'contains': ['7776.z1', '7776.bt1', '7776.cr1', '11664.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 39366316080, 6227827207], 'label': '46656.ir.3888.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.em1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714818
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ia1', '1296.if1', '1296.ig1', '1296.ih1', '1944.z1', '1944.cx1', '1944.fk1'], 'contains': ['7776.z1', '7776.bv1', '7776.cn1', '11664.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41091120, 40323593520, 6227827207], 'label': '46656.ir.3888.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.en1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714819
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ii1', '1296.ij1', '1296.jh1', '1944.r1', '1944.bf1', '1944.ff1', '1944.ga1', '1944.gb1', '1944.gc1', '1944.gu1'], 'contains': ['7776.ba1', '7776.bf1', '11664.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1174320, 6267744000, 435], 'label': '46656.ir.3888.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '3888.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.eo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714820
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.eg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ij1', '1296.ji1', '1944.bg1', '1944.bw1', '1944.dr1', '1944.gd1', '1944.ge1', '1944.gf1', '1944.hf1'], 'contains': ['7776.bb1', '7776.bi1', '11664.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 6267744000], 'label': '46656.ir.3888.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ep1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714821
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ik1', '1296.jp1', '1944.ba1', '1944.ca1', '1944.fm1', '1944.gd1', '1944.gg1', '1944.gh1', '1944.hg1'], 'contains': ['7776.bb1', '7776.bm1', '11664.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 39957120, 1481684400], 'label': '46656.ir.3888.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.eq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714822
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.il1', '1296.im1', '1296.in1', '1296.jj1', '1296.jk1', '1944.n1', '1944.bh1', '1944.fn1', '1944.ga1', '1944.gi1', '1944.gj1', '1944.gy1'], 'contains': ['7776.ba1', '7776.bo1', '7776.cg1', '11664.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [39957555, 39957120, 1134007], 'label': '46656.ir.3888.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '3888.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.er1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714823
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.il1', '1296.jl1', '1296.jn1', '1944.bi1', '1944.bq1', '1944.fo1', '1944.ge1', '1944.gk1', '1944.gl1', '1944.hg1'], 'contains': ['7776.bb1', '7776.bp1', '7776.ch1', '11664.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 1134007, 1481684400], 'label': '46656.ir.3888.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.es1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714824
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.il1', '1296.im1', '1296.jm1', '1296.jo1', '1944.bj1', '1944.fp1', '1944.gm1'], 'contains': ['7776.bc1', '7776.bq1', '7776.ck1', '11664.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [1521641955, 39957120, 1134007], 'label': '46656.ir.3888.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '3888.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.et1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714825
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.ch1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ik1', '1296.io1', '1296.jq1', '1944.u1', '1944.bb1', '1944.fq1', '1944.gb1', '1944.gn1', '1944.go1', '1944.gy1'], 'contains': ['7776.ba1', '7776.bo1', '11664.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39916807, 39957555, 39957120], 'label': '46656.ir.3888.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '3888.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.eu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714826
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ip1', '1296.jr1', '1944.bk1', '1944.cb1', '1944.cv1', '1944.ge1', '1944.gg1', '1944.gp1', '1944.hh1'], 'contains': ['7776.bb1', '7776.br1', '11664.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 6227827207], 'label': '46656.ir.3888.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ev1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714827
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '24.k1', '24.q1', '24.u1'], 'contains': ['96.c1', '96.d1', '96.y1', '144.g1', '144.z1', '144.ba1', '144.bb1', '144.bc1', '144.bd1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 1134000, 39957127], 'label': '46656.ir.48.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714828
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ip1', '1296.iq1', '1296.js1', '1944.v1', '1944.bl1', '1944.fe1', '1944.ga1', '1944.gn1', '1944.gq1', '1944.gz1'], 'contains': ['7776.ba1', '7776.bu1', '11664.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1174320, 6227827207, 104], 'label': '46656.ir.3888.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '3888.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ew1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714829
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ir1', '1296.is1', '1296.it1', '1296.jt1', '1944.u1', '1944.bh1', '1944.fi1', '1944.fr1', '1944.gc1', '1944.gq1', '1944.gr1'], 'contains': ['7776.ba1', '7776.ca1', '11664.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [41050807, 39957555, 39957120], 'label': '46656.ir.3888.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '3888.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ex1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714830
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ir1', '1296.jv1', '1944.bi1', '1944.ca1', '1944.em1', '1944.fs1', '1944.gf1', '1944.gp1', '1944.gs1'], 'contains': ['7776.bb1', '7776.cb1', '11664.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41050807, 39957120, 1481684400], 'label': '46656.ir.3888.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ey1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714831
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ir1', '1296.is1', '1296.ju1', '1944.bj1', '1944.ft1', '1944.gt1'], 'contains': ['7776.bc1', '7776.cd1', '11664.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [41050807, 39957120, 1521641624], 'label': '46656.ir.3888.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '3888.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ez1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714832
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.iu1', '1296.iv1', '1296.iw1', '1296.jw1', '1944.v1', '1944.bm1', '1944.ff1', '1944.fn1', '1944.go1', '1944.gr1', '1944.hc1'], 'contains': ['7776.ba1', '7776.co1', '11664.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 1174320, 435], 'label': '46656.ir.3888.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '3888.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fa1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714833
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.iu1', '1296.jx1', '1944.bn1', '1944.cb1', '1944.dr1', '1944.fo1', '1944.gh1', '1944.gs1', '1944.hi1'], 'contains': ['7776.bb1', '7776.cp1', '11664.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267744007, 268280812800, 1174320], 'label': '46656.ir.3888.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714834
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.iu1', '1296.iv1', '1296.jy1', '1944.bo1', '1944.fp1', '1944.gt1'], 'contains': ['7776.bc1', '7776.cs1', '11664.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [6267744007, 355419187635, 1174320], 'label': '46656.ir.3888.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '3888.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714835
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.cj1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kn1', '1296.ix1', '1296.jb1', '1296.jd1', '1944.w1', '1944.bc1', '1944.fg1', '1944.gi1', '1944.gn1', '1944.gr1', '1944.gu1'], 'contains': ['7776.ba1', '11664.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6227464320, 1174320, 435], 'label': '46656.ir.3888.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '3888.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714836
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ko1', '1296.iy1', '1296.je1', '1944.w1', '1944.bf1', '1944.fh1', '1944.fu1', '1944.gj1', '1944.go1', '1944.gq1'], 'contains': ['7776.ba1', '11664.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267381120, 1174320, 104], 'label': '46656.ir.3888.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.o1', 'old_label': '3888.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fe1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714837
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kp1', '1296.iz1', '1296.jf1', '1944.x1', '1944.bl1', '1944.fg1', '1944.fq1', '1944.gc1', '1944.gj1', '1944.hc1'], 'contains': ['7776.ba1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1174320, 6227464327, 104], 'label': '46656.ir.3888.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '3888.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ff1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714838
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.r1', '24.s1', '24.t1', '24.u1', '24.v1', '24.w1'], 'contains': ['96.d1', '96.o1', '144.be1', '144.bf1', '144.bg1', '144.bh1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 325, 1481684400, 39916800, 269279866800, 1521641624], 'label': '46656.ir.48.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '576.8389'}
  • id: 216714839
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kq1', '1296.ja1', '1296.jc1', '1296.jg1', '1944.x1', '1944.bm1', '1944.fh1', '1944.fr1', '1944.gb1', '1944.gi1', '1944.gz1'], 'contains': ['7776.ba1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267381127, 1174320, 104], 'label': '46656.ir.3888.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.m1', 'old_label': '3888.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714840
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.em1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kt1', '1296.ix1', '1944.bd1', '1944.cc1', '1944.dt1', '1944.gg1', '1944.gk1', '1944.gs1', '1944.hf1'], 'contains': ['7776.bb1', '11664.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 6227464320, 1174320], 'label': '46656.ir.3888.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714841
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.ep1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.ku1', '1296.iy1', '1944.bg1', '1944.cc1', '1944.dw1', '1944.fv1', '1944.gh1', '1944.gl1', '1944.gp1'], 'contains': ['7776.bb1', '11664.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381120, 268280812800, 1174320], 'label': '46656.ir.3888.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714842
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kv1', '1296.iz1', '1944.bk1', '1944.cd1', '1944.dt1', '1944.fm1', '1944.gf1', '1944.gl1', '1944.hi1'], 'contains': ['7776.bb1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [268280812800, 1174320, 6227464327], 'label': '46656.ir.3888.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714843
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.kw1', '1296.ja1', '1944.bn1', '1944.cd1', '1944.dw1', '1944.fs1', '1944.gd1', '1944.gk1', '1944.hh1'], 'contains': ['7776.bb1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320], 'label': '46656.ir.3888.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '3888.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714844
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.ja1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.kr1', '1296.ix1', '1296.jb1', '1944.be1', '1944.gm1', '1944.gt1'], 'contains': ['7776.bc1', '11664.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6227464320, 1174320, 268280812904], 'label': '46656.ir.3888.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '3888.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714845
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['432.ks1', '1296.ja1', '1296.jc1', '1944.bo1', '1944.ft1', '1944.gm1'], 'contains': ['7776.bc1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [355419187635, 6267381127, 1174320], 'label': '46656.ir.3888.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '3888.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714846
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jh1', '1296.ji1', '1296.kd1', '1944.t1', '1944.ec1', '1944.gv1'], 'contains': ['7776.be1', '7776.bg1', '7776.bk1', '11664.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174320, 6267744000], 'label': '46656.ir.3888.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '3888.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714847
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jj1', '1296.jm1', '1296.jn1', '1296.ke1', '1944.c1', '1944.cg1', '1944.hg1'], 'contains': ['7776.bd1', '7776.bm1', '7776.ch1', '11664.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39957120, 1134007, 37885034880], 'label': '46656.ir.3888.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '3888.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714848
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jk1', '1296.jl1', '1296.jo1', '1296.ke1', '1944.d1', '1944.fx1', '1944.gv1'], 'contains': ['7776.be1', '7776.bn1', '7776.cj1', '11664.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [387037284480, 39957120, 1134007], 'label': '46656.ir.3888.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714849
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.bb1', '16.b1', '24.z1'], 'contains': ['96.e1', '96.i1', '96.u1', '144.bi1', '144.bp1', '144.bq1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [624190336641, 39366316080, 7, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.48.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '48.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216714850
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jp1', '1296.jq1', '1296.kf1', '1944.y1', '1944.cf1', '1944.hg1'], 'contains': ['7776.bd1', '7776.bm1', '7776.bp1', '11664.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39957120, 37885034880], 'label': '46656.ir.3888.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '3888.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714851
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jr1', '1296.js1', '1296.kg1', '1944.z1', '1944.de1', '1944.gv1'], 'contains': ['7776.be1', '7776.bt1', '7776.bv1', '11664.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 1174320, 6227827207], 'label': '46656.ir.3888.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714852
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jt1', '1296.ju1', '1296.jv1', '1296.kh1', '1944.y1', '1944.cg1', '1944.em1'], 'contains': ['7776.bd1', '7776.bz1', '7776.cb1', '11664.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [41050807, 39957120, 37885034880], 'label': '46656.ir.3888.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '3888.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714853
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.jw1', '1296.jx1', '1296.jy1', '1296.ki1', '1944.z1', '1944.ec1', '1944.fx1'], 'contains': ['7776.be1', '7776.cn1', '7776.cr1', '11664.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320], 'label': '46656.ir.3888.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ft1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714854
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.jz1', '1296.ka1', '1296.kb1', '1296.kc1', '1944.bx1', '1944.fi1', '1944.fu1', '1944.gu1', '1944.gy1', '1944.gz1', '1944.hc1'], 'contains': ['7776.ba1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957555, 39957120, 41050800], 'label': '46656.ir.3888.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '3888.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714855
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1', '1296.jz1', '1944.by1', '1944.el1', '1944.fy1', '1944.gw1', '1944.gx1', '1944.ha1', '1944.hd1'], 'contains': ['11664.bi1', '15552.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [655477406640, 268240936320, 269202528000], 'label': '46656.ir.3888.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '3888.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fv1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714856
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gt1', '1296.jz1', '1296.ka1', '1944.bz1', '1944.hb1', '1944.he1'], 'contains': ['11664.bi1', '15552.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [268240936320, 195089010864, 269202528000], 'label': '46656.ir.3888.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bq1', 'old_label': '3888.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fw1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 216714857
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.z1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kc1', '1296.kn1', '1944.ch1', '1944.em1', '1944.fv1', '1944.hf1', '1944.hg1', '1944.hh1', '1944.hi1'], 'contains': ['7776.bb1', '7776.bd1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 37885034880], 'label': '46656.ir.3888.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '3888.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714858
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ko1', '1296.kw1', '1296.kx1', '1944.a1', '1944.fw1', '1944.gv1'], 'contains': ['7776.bg1', '7776.bn1', '7776.bt1', '11664.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916807, 39366316080, 6227827207], 'label': '46656.ir.3888.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fy1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714859
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ko1', '1296.kp1', '1296.ky1', '1296.kz1', '1944.m1', '1944.fj1', '1944.ga1'], 'contains': ['7776.bf1', '7776.bo1', '7776.bu1', '11664.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [39916807, 6227827207, 435], 'label': '46656.ir.3888.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '3888.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.fz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714860
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.v1', '16.c1', '24.z1'], 'contains': ['96.e1', '96.m1', '96.z1', '144.bj1', '144.br1', '144.bs1'], 'core': '864.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [41091120, 39366316080, 622713012218, 7, 325, 1481684400, 269279866800], 'label': '46656.ir.48.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '48.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216714861
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kq1', '1296.kr1', '1296.ks1', '1296.la1', '1296.lb1', '1296.lc1', '1296.lj1', '1944.o1', '1944.fd1', '1944.ga1'], 'contains': ['7776.bf1', '7776.bu1', '7776.cg1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [6227827207, 41091127, 435], 'label': '46656.ir.3888.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.j1', 'old_label': '3888.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ga1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714862
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kq1', '1296.ld1', '1296.lf1', '1296.lg1', '1944.p1', '1944.cx1', '1944.gv1'], 'contains': ['7776.bg1', '7776.bv1', '7776.cj1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [40323593520, 6227827207, 41091127], 'label': '46656.ir.3888.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714863
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kq1', '1296.kr1', '1296.le1', '1296.lh1', '1296.li1', '1944.q1'], 'contains': ['7776.bh1', '7776.bw1', '7776.cm1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [40323593624, 6227827207, 41091127], 'label': '46656.ir.3888.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.q1', 'old_label': '3888.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714864
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kt1', '1296.ku1', '1296.kv1', '1296.lk1', '1296.ln1', '1944.o1', '1944.ff1', '1944.fj1'], 'contains': ['7776.bf1', '7776.ca1', '7776.co1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [6267744007, 1174327, 435], 'label': '46656.ir.3888.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.j1', 'old_label': '3888.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714865
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kt1', '1296.ll1', '1296.lo1', '1944.p1', '1944.ec1', '1944.fw1'], 'contains': ['7776.bg1', '7776.cc1', '7776.cr1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 1174327, 40323593520], 'label': '46656.ir.3888.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.ge1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714866
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.kt1', '1296.ku1', '1296.lm1', '1296.lp1', '1944.q1'], 'contains': ['7776.bh1', '7776.ce1', '7776.cu1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [6267744007, 1174327, 40323593955], 'label': '46656.ir.3888.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.q1', 'old_label': '3888.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714867
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kw1', '1296.ky1', '1296.lq1', '1944.b1', '1944.fk1', '1944.gv1'], 'contains': ['7776.bk1', '7776.bn1', '7776.bv1', '11664.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 40323593520, 6227827207], 'label': '46656.ir.3888.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '3888.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714868
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kx1', '1296.kz1', '1296.lq1', '1944.bp1', '1944.fl1', '1944.ge1'], 'contains': ['7776.bi1', '7776.bp1', '7776.br1', '11664.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 268280812800, 6227827207], 'label': '46656.ir.3888.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '3888.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714869
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.la1', '1296.ld1', '1296.le1', '1296.lr1', '1944.bv1', '1944.ci1', '1944.ge1'], 'contains': ['7776.bi1', '7776.br1', '7776.ch1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [268280812800, 6227827207, 41091127], 'label': '46656.ir.3888.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '3888.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714870
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.lb1', '1296.lg1', '1296.lh1', '1296.lr1', '1296.ls1', '1944.cj1'], 'contains': ['7776.bj1', '7776.bs1', '7776.ci1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [387999647280, 6227827207, 41091127], 'label': '46656.ir.3888.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.by1', 'old_label': '3888.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714871
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.bc1', '16.d1', '24.z1'], 'contains': ['96.e1', '96.s1', '96.bc1', '144.bk1', '144.bu1', '144.bv1', '144.bw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [6267744007, 39366316080, 622713012218, 7, 325, 1481684400, 269279866800], 'label': '46656.ir.48.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '48.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216714872
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.lc1', '1296.lf1', '1296.li1', '1296.lr1', '1944.s1', '1944.ck1', '1944.gv1'], 'contains': ['7776.bk1', '7776.bt1', '7776.cj1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39366316080, 6227827207, 41091127], 'label': '46656.ir.3888.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714873
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.dq1', '1296.lj1', '1296.ls1', '1944.cw1'], 'contains': ['7776.bl1', '7776.bx1', '7776.cf1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6227827207, 93575951280, 41091127], 'label': '46656.ir.3888.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '3888.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714874
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.lk1', '1296.ll1', '1296.lm1', '1296.lt1', '1944.bv1', '1944.dr1', '1944.fl1'], 'contains': ['7776.bi1', '7776.bz1', '7776.cp1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 1174327, 268280812800], 'label': '46656.ir.3888.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '3888.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714875
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ln1', '1296.lo1', '1296.lp1', '1296.lt1', '1944.s1', '1944.ec1', '1944.fk1'], 'contains': ['7776.bk1', '7776.cc1', '7776.cn1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080], 'label': '46656.ir.3888.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '3888.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714876
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.mg1', '432.mi1', '432.mk1', '1944.ce1', '1944.ea1', '1944.fz1'], 'contains': ['7776.bz1', '11664.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [268280812800, 1174789, 6227752218], 'label': '46656.ir.3888.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.k1', 'old_label': '3888.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.go1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714877
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3888.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.mh1', '432.mj1', '432.ml1', '1944.ce1', '1944.eb1', '1944.fz1'], 'contains': ['7776.bz1', '11664.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267669018, 268280812800, 1174789], 'label': '46656.ir.3888.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.k1', 'old_label': '3888.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.gp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714896
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.f1', '1728.h1', '1728.u1', '1728.bc1', '1728.bd1', '1728.be1', '1728.bf1', '1728.bg1', '2592.da1', '2592.dx1', '2592.fk1'], 'contains': ['15552.c1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [301891126320, 269279867235], 'label': '46656.ir.5184.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.l1', 'old_label': '5184.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714878
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.b1', 'complements': ['9.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1728.q1', '1728.r1', '1728.s1', '1728.t1', '2592.a1', '2592.f1', '2592.be1', '2592.bw1', '2592.ch1', '2592.cr1', '2592.do1', '2592.ef1', '2592.ep1', '2592.fd1', '2592.gg1'], 'contains': ['15552.a1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [325, 104], 'label': '46656.ir.5184.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5184.a1', 'normal_contained_in': ['192.a1', '2592.a1'], 'normal_contains': ['46656.a1'], 'normalizer': '1.a1', 'old_label': '5184.a1', 'projective_image': '46656.ir', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1296.3490', 'quotient_action_kernel_order': 1296, 'quotient_fusion': None, 'short_label': '5184.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714879
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.b1', '1728.c1', '1728.d1', '1728.e1', '1728.q1', '2592.b1', '2592.k1', '2592.u1', '2592.y1', '2592.bx1', '2592.cf1', '2592.ci1', '2592.cs1', '2592.dg1', '2592.dm1', '2592.dq1', '2592.eg1', '2592.el1', '2592.ex1', '2592.fy1'], 'contains': ['15552.a1', '15552.b1', '15552.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [37885034880, 31658054835], 'label': '46656.ir.5184.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '5184.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714880
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.b1', '1728.f1', '1728.g1', '1728.h1', '1728.i1', '1728.j1', '1728.k1', '1728.l1', '1728.r1', '2592.v1', '2592.z1', '2592.by1', '2592.ct1', '2592.dr1', '2592.ey1', '2592.fz1'], 'contains': ['15552.a1', '15552.c1', '15552.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [301891126320, 435], 'label': '46656.ir.5184.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '5184.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714881
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.b1', '1728.e1', '1728.f1', '1728.m1', '1728.n1', '1728.o1', '1728.s1', '2592.c1', '2592.w1', '2592.ba1', '2592.bk1', '2592.bz1', '2592.cj1', '2592.cp1', '2592.cu1', '2592.dh1', '2592.ds1', '2592.eb1', '2592.em1', '2592.ez1', '2592.fr1', '2592.ga1'], 'contains': ['15552.a1', '15552.d1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 104], 'label': '46656.ir.5184.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '5184.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714882
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.c1', '12.bg1', '12.bh1', '12.bj1', '12.bu1', '12.bv1', '12.bz1', '18.v1', '54.bc1', '54.bg1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 7, 41051125, 39917299, 269279866800, 1521641624], 'label': '46656.ir.6.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714883
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.e1', '24.bb1', '24.bc1', '24.bd1', '24.be1', '24.bf1', '24.bg1'], 'contains': ['96.a1', '96.h1', '96.w1', '144.bp1', '144.bx1', '144.by1', '144.bz1', '144.ca1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.48.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216714884
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.d1', '1728.g1', '1728.m1', '1728.n1', '1728.q1', '2592.d1', '2592.bb1', '2592.cg1', '2592.dn1', '2592.en1', '2592.fa1', '2592.gb1'], 'contains': ['15552.a1', '15552.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [325, 1481684504], 'label': '46656.ir.5184.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '5184.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714885
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.c1', '1728.g1', '1728.m1', '1728.o1', '1728.p1', '1728.r1', '2592.bc1', '2592.fb1', '2592.gc1'], 'contains': ['15552.a1', '15552.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [294706903784, 325], 'label': '46656.ir.5184.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '5184.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714886
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.c1', '1728.d1', '1728.g1', '1728.h1', '1728.n1', '1728.o1', '1728.s1', '2592.e1', '2592.bd1', '2592.cq1', '2592.ec1', '2592.eo1', '2592.fc1', '2592.gd1'], 'contains': ['15552.a1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316405, 104], 'label': '46656.ir.5184.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '5184.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714887
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.jz1', '1728.i1', '1728.p1', '1728.t1', '2592.x1', '2592.bl1', '2592.bu1', '2592.cv1', '2592.ed1', '2592.eu1', '2592.ge1'], 'contains': ['15552.a1', '15552.h1', '15552.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [643350723201, 104], 'label': '46656.ir.5184.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.de1', 'old_label': '5184.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714888
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.ka1', '1728.j1', '1728.p1', '1728.t1', '2592.bv1', '2592.ee1', '2592.gf1'], 'contains': ['15552.a1', '15552.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [722937560115, 104], 'label': '46656.ir.5184.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ex1', 'old_label': '5184.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714889
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.a1', '1728.b1', '1728.u1', '2592.l1', '2592.p1', '2592.bf1', '2592.bm1', '2592.cc1', '2592.ck1', '2592.cw1', '2592.dc1', '2592.di1', '2592.dp1', '2592.dt1', '2592.eh1', '2592.fe1', '2592.fs1', '2592.gh1'], 'contains': ['15552.b1', '15552.c1', '15552.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [269279866800, 37885034880], 'label': '46656.ir.5184.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '5184.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714890
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.d1', '1728.e1', '1728.u1', '1728.v1', '1728.v2', '1728.w1', '2592.g1', '2592.m1', '2592.cl1', '2592.dj1', '2592.ei1', '2592.eq1', '2592.ff1'], 'contains': ['15552.b1', '15552.e1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684504, 37885034880], 'label': '46656.ir.5184.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.u1', 'old_label': '5184.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714891
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.b1', '1728.c1', '1728.u1', '1728.v1', '1728.v2', '1728.w1', '2592.n1', '2592.bg1', '2592.cx1', '2592.du1', '2592.ej1', '2592.fg1', '2592.gi1'], 'contains': ['15552.b1', '15552.f1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [37885034880, 270715783395], 'label': '46656.ir.5184.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '5184.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714892
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.a1', '1728.e1', '1728.w1', '2592.h1', '2592.o1', '2592.q1', '2592.bn1', '2592.cd1', '2592.cm1', '2592.co1', '2592.cy1', '2592.df1', '2592.dk1', '2592.dv1', '2592.ek1', '2592.er1', '2592.fh1', '2592.ft1'], 'contains': ['15552.b1', '15552.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 37885034880], 'label': '46656.ir.5184.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '5184.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.m1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 216714893
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.a1', '1728.f1', '1728.x1', '1728.y1', '1728.z1', '1728.ba1', '1728.bb1', '2592.r1', '2592.bo1', '2592.ce1', '2592.cz1', '2592.dw1', '2592.fi1', '2592.fu1'], 'contains': ['15552.c1', '15552.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 269279866800], 'label': '46656.ir.5184.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '5184.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714894
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '24.bh1', '24.bi1', '24.bj1'], 'contains': ['96.f1', '96.k1', '96.x1', '144.bq1', '144.ca1', '144.cb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [40323593624, 7, 325, 270715782960, 40323593520, 6227827207, 461482882830], 'label': '46656.ir.48.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '48.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216714895
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.b1', '1728.g1', '1728.u1', '1728.x1', '1728.bc1', '2592.bh1', '2592.fj1', '2592.gj1'], 'contains': ['15552.c1', '15552.e1', '15552.f1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1481684835, 301891126320], 'label': '46656.ir.5184.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '5184.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714897
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.dj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.i1', '1728.y1', '1728.bd1', '2592.s1', '2592.bp1', '2592.ca1', '2592.dd1', '2592.dy1', '2592.ev1', '2592.gk1'], 'contains': ['15552.c1', '15552.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [301891126320, 655477406640], 'label': '46656.ir.5184.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '5184.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714898
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.i1', '1728.j1', '1728.z1', '1728.bd1', '1728.be1', '2592.cb1', '2592.dz1', '2592.gl1'], 'contains': ['15552.c1', '15552.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [438489677184, 388956924720], 'label': '46656.ir.5184.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bp1', 'old_label': '5184.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 216714899
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.dn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1728.k1', '1728.ba1', '1728.bf1', '2592.t1', '2592.de1', '2592.gm1'], 'contains': ['15552.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [301891126320, 623823424560], 'label': '46656.ir.5184.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '5184.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.s1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 216714900
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.k1', '1728.l1', '1728.bb1', '1728.bf1', '1728.bg1', '2592.gn1'], 'contains': ['15552.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [387999647280, 435907060188], 'label': '46656.ir.5184.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bi1', 'old_label': '5184.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.t1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 216714901
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.b1', '1728.m1', '1728.w1', '1728.x1', '1728.bh1', '1728.bh2', '2592.bi1', '2592.bq1', '2592.cn1', '2592.dl1', '2592.fl1', '2592.fv1', '2592.go1'], 'contains': ['15552.d1', '15552.e1', '15552.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 355419187304], 'label': '46656.ir.5184.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.ch1', 'old_label': '5184.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714902
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.e1', '1728.n1', '1728.u1', '1728.x1', '1728.bh1', '1728.bh2', '2592.i1', '2592.br1', '2592.db1', '2592.ea1', '2592.es1', '2592.fm1', '2592.fw1'], 'contains': ['15552.d1', '15552.e1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 1481684504], 'label': '46656.ir.5184.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '5184.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714903
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.f1', '1728.o1', '1728.u1', '1728.w1', '1728.x1', '1728.bh1', '1728.bh2', '2592.bs1', '2592.fn1', '2592.fx1'], 'contains': ['15552.d1', '15552.f1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39366316080, 270715783064], 'label': '46656.ir.5184.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '5184.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714904
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1728.c1', '1728.g1', '1728.m1', '1728.v1', '1728.bc1', '1728.bh1', '1728.bh2', '2592.bj2', '2592.fo1', '2592.gp2'], 'contains': ['15552.e1', '15552.f1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [39366316405, 382729979624], 'label': '46656.ir.5184.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '5184.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714905
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '24.bh1', '24.bk1', '24.bl1'], 'contains': ['96.f1', '96.l1', '96.bb1', '144.br1', '144.cc1', '144.cf1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 325, 270715782960, 40323593520, 461482882830], 'label': '46656.ir.48.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216714906
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.c1', '1728.g1', '1728.m1', '1728.v2', '1728.bc1', '1728.bh1', '1728.bh2', '2592.bj1', '2592.fo2', '2592.gp1'], 'contains': ['15552.e1', '15552.f1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [301891126645, 1481684504], 'label': '46656.ir.5184.x2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bi1', 'old_label': '5184.x2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.x2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714907
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.d1', '1728.n1', '1728.v1', '1728.bc1', '1728.bh2', '2592.j1', '2592.et1', '2592.fp1'], 'contains': ['15552.e1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39366316405, 1481684504], 'label': '46656.ir.5184.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.j1', 'old_label': '5184.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714908
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.d1', '1728.n1', '1728.v2', '1728.bc1', '1728.bh1', '2592.j2', '2592.et2', '2592.fp2'], 'contains': ['15552.e1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1481684725, 33139370984], 'label': '46656.ir.5184.y2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.q1', 'old_label': '5184.y2', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.y2', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 216714909
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.h1', '1728.o1', '1728.v1', '1728.v2', '1728.bc1', '1728.bh1', '1728.bh2', '2592.fq1'], 'contains': ['15552.f1', '15552.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [270715783064, 39366316405], 'label': '46656.ir.5184.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.c1', 'old_label': '5184.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714910
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.i1', '1728.p1', '2592.bt1', '2592.ew1', '2592.gq1'], 'contains': ['15552.f1', '15552.h1', '15552.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [643350723201, 387999647384], 'label': '46656.ir.5184.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.eg1', 'old_label': '5184.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714911
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5184.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1728.j1', '1728.p1', '2592.gr1'], 'contains': ['15552.f1', '15552.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [387999647605, 463289990028], 'label': '46656.ir.5184.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.ec1', 'old_label': '5184.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714912
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.a1', '1944.b1', '1944.m1', '1944.bp1', '2916.a1', '2916.b1', '2916.c1'], 'contains': ['11664.a1', '11664.b1', '11664.e1', '11664.h1', '11664.k1', '11664.s1', '11664.bj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [7, 39916800, 6227827207], 'label': '46656.ir.5832.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '5832.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714913
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.c1', '1944.d1', '1944.n1', '1944.bq1', '2916.c1', '2916.d1', '2916.e1', '2916.f1', '2916.g1', '2916.h1', '2916.s1'], 'contains': ['11664.a1', '11664.c1', '11664.f1', '11664.i1', '11664.j1', '11664.w1', '11664.z1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 7, 1134000], 'label': '46656.ir.5832.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714914
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.m1', '1944.e1', '1944.i1', '1944.br1', '2916.a1', '2916.d1', '2916.m1'], 'contains': ['11664.a1', '11664.l1', '11664.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [499, 444, 39916800], 'label': '46656.ir.5832.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '5832.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714915
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.n1', '1944.f1', '1944.g1', '1944.bs1', '2916.f1', '2916.m1', '2916.n1'], 'contains': ['11664.a1', '11664.m1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [444, 40320, 39957619], 'label': '46656.ir.5832.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '5832.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714916
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.f1', '24.r1', '24.bg1', '24.bo1', '24.bp1', '24.bq1', '24.br1', '24.bs1', '24.bt1', '24.bu1', '24.bv1', '24.bw1', '24.bx1', '24.by1'], 'contains': ['96.a1', '96.o1', '96.y1', '144.bt1', '144.cg1', '144.ch1', '144.ci1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 325, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.48.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216714917
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.o1', '1944.j1', '1944.k1', '1944.bt1', '2916.a1', '2916.b1', '2916.g1'], 'contains': ['11664.a1', '11664.n1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [469, 39916800, 6227827818], 'label': '46656.ir.5832.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '5832.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714918
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.p1', '1944.h1', '1944.l1', '1944.bu1', '2916.b1', '2916.d1', '2916.n1'], 'contains': ['11664.a1', '11664.o1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [444, 1134000, 39957619], 'label': '46656.ir.5832.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714919
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.o1', '1944.p1', '1944.q1', '1944.s1', '1944.bv1', '2916.c1'], 'contains': ['11664.b1', '11664.e1', '11664.f1', '11664.t1', '11664.u1', '11664.bk1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [1174327, 39916800, 6227827207], 'label': '46656.ir.5832.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '5832.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714920
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.r1', '1944.t1', '1944.bw1', '2916.c1', '2916.i1', '2916.t1'], 'contains': ['11664.b1', '11664.c1', '11664.r1', '11664.v1', '11664.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174320, 39916800, 6227827200], 'label': '46656.ir.5832.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '5832.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714921
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.u1', '1944.y1', '1944.ca1', '2916.i1', '2916.j1', '2916.s1'], 'contains': ['11664.c1', '11664.d1', '11664.w1', '11664.ba1', '11664.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [41050807, 39957120, 1134000], 'label': '46656.ir.5832.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714922
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.v1', '1944.z1', '1944.cb1', '2916.c1', '2916.j1', '2916.u1'], 'contains': ['11664.c1', '11664.e1', '11664.x1', '11664.bb1', '11664.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [1174320, 39916800, 6227827207], 'label': '46656.ir.5832.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714923
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bh1', '1944.w1', '1944.cc1', '2916.e1', '2916.j1', '2916.t1'], 'contains': ['11664.c1', '11664.be1', '11664.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 1174320, 39916800], 'label': '46656.ir.5832.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '5832.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714924
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bi1', '1944.x1', '1944.cd1', '2916.e1', '2916.i1', '2916.u1'], 'contains': ['11664.c1', '11664.bg1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 1174320, 39916800], 'label': '46656.ir.5832.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714925
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.bj1', '648.bk1', '648.bl1', '1944.ce1', '2916.h1'], 'contains': ['11664.f1', '11664.bm1', '11664.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [6267669018, 1174789, 39916800], 'label': '46656.ir.5832.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.c1', 'old_label': '5832.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714926
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.ba1', '1944.bb1', '1944.cf1', '2916.k1', '2916.l1', '2916.m1', '2916.n1', '2916.o1', '2916.p1', '2916.s1'], 'contains': ['11664.a1', '11664.d1', '11664.g1', '11664.j1', '11664.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 7, 39916800], 'label': '46656.ir.5832.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714927
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.e1', '24.bb1', '24.bo1', '24.bz1', '24.ca1', '24.cb1', '24.cc1'], 'contains': ['96.a1', '96.p1', '96.bg1', '144.bu1', '144.cj1', '144.ck1', '144.cl1', '144.cm1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.48.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216714928
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dl1', '1944.bc1', '1944.bd1', '1944.be1', '2916.k1', '2916.q1', '2916.t1'], 'contains': ['11664.g1', '11664.v1', '11664.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174320, 6227827200, 40320], 'label': '46656.ir.5832.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '5832.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714929
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dm1', '1944.bf1', '1944.bg1', '2916.l1', '2916.r1', '2916.t1'], 'contains': ['11664.g1', '11664.y1', '11664.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 1174320, 40320], 'label': '46656.ir.5832.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '5832.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714930
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.bh1', '1944.bi1', '1944.bj1', '1944.cg1', '2916.q1', '2916.r1', '2916.s1'], 'contains': ['11664.d1', '11664.f1', '11664.g1', '11664.z1', '11664.bc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [41050807, 39957120, 39916800], 'label': '46656.ir.5832.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714931
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.do1', '1944.bk1', '1944.bl1', '2916.k1', '2916.r1', '2916.u1'], 'contains': ['11664.g1', '11664.bb1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [1174320, 40320, 6227827207], 'label': '46656.ir.5832.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714932
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.dp1', '1944.bm1', '1944.bn1', '1944.bo1', '2916.l1', '2916.q1', '2916.u1'], 'contains': ['11664.g1', '11664.bd1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 1174320, 40320], 'label': '46656.ir.5832.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714933
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.bx1', '1944.by1', '1944.bz1', '1944.ch1', '2916.s1', '2916.t1', '2916.u1'], 'contains': ['11664.c1', '11664.g1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 39916800], 'label': '46656.ir.5832.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '5832.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714934
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.ci1', '1944.cj1', '1944.ck1', '1944.cw1', '1944.cx1', '1944.fd1', '2916.c1', '2916.v1', '2916.w1'], 'contains': ['11664.h1', '11664.i1', '11664.k1', '11664.r1', '11664.u1', '11664.x1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [41091120, 7, 6227827207], 'label': '46656.ir.5832.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '5832.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714935
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ha1', '1944.cl1', '1944.cp1', '1944.cr1', '1944.cy1', '1944.dc1', '2916.a1', '2916.v1', '2916.x1'], 'contains': ['11664.h1', '11664.l1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [499, 443130957804, 444], 'label': '46656.ir.5832.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '5832.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714936
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hb1', '1944.cm1', '1944.cs1', '1944.cz1', '2916.a1', '2916.w1', '2916.y1'], 'contains': ['11664.h1', '11664.m1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [40819, 443130957804, 444], 'label': '46656.ir.5832.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '5832.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714937
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hc1', '1944.cn1', '1944.ct1', '1944.da1', '2916.b1', '2916.w1', '2916.x1'], 'contains': ['11664.h1', '11664.n1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [180790853484, 41051299, 444], 'label': '46656.ir.5832.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '5832.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714938
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.bh1', '24.cd1', '24.ce1'], 'contains': ['96.f1', '96.q1', '96.bh1', '144.bv1', '144.cl1', '144.cn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 270715782960, 104, 716634334350], 'label': '46656.ir.48.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216714939
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hd1', '1944.co1', '1944.cq1', '1944.cu1', '1944.db1', '1944.dd1', '2916.b1', '2916.v1', '2916.y1'], 'contains': ['11664.h1', '11664.o1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [180790853484, 41091619, 444], 'label': '46656.ir.5832.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '5832.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714940
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.cv1', '1944.de1', '1944.fe1', '2916.c1', '2916.k1', '2916.x1', '2916.y1', '2916.z1', '2916.ba1', '2916.bb1'], 'contains': ['11664.h1', '11664.j1', '11664.t1', '11664.v1', '11664.bb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [7, 1174320, 6227827207], 'label': '46656.ir.5832.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714941
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hf1', '1944.df1', '1944.dh1', '1944.dl1', '1944.dn1', '2916.d1', '2916.v1'], 'contains': ['11664.i1', '11664.l1', '11664.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41091120, 499, 444], 'label': '46656.ir.5832.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '5832.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714942
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hg1', '1944.di1', '1944.dj1', '1944.do1', '2916.d1', '2916.f1', '2916.w1'], 'contains': ['11664.i1', '11664.m1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [41091120, 444, 39957619], 'label': '46656.ir.5832.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714943
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hh1', '1944.dg1', '1944.dk1', '1944.dm1', '1944.dp1', '1944.dq1', '2916.g1', '2916.v1', '2916.w1'], 'contains': ['11664.i1', '11664.n1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [41091120, 469, 6227827818], 'label': '46656.ir.5832.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '5832.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714944
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.dr1', '1944.ec1', '1944.ff1', '2916.c1', '2916.l1', '2916.bc1', '2916.bd1', '2916.be1', '2916.bf1', '2916.bo1'], 'contains': ['11664.j1', '11664.k1', '11664.y1', '11664.bd1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 7, 1174320], 'label': '46656.ir.5832.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714945
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hj1', '1944.ds1', '1944.ed1', '1944.eh1', '2916.d1', '2916.m1', '2916.x1', '2916.bc1', '2916.bg1', '2916.bh1', '2916.bp1'], 'contains': ['11664.j1', '11664.l1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 499, 39957564], 'label': '46656.ir.5832.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714946
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fl1', '1944.dt1', '1944.fg1', '2916.e1', '2916.k1', '2916.bg1', '2916.bi1', '2916.bj1', '2916.bk1', '2916.bo1'], 'contains': ['11664.j1', '11664.be1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [7, 1174320, 6227464327], 'label': '46656.ir.5832.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714947
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hl1', '1944.dv1', '1944.ee1', '1944.ei1', '2916.d1', '2916.n1', '2916.y1', '2916.bd1', '2916.bi1', '2916.bl1', '2916.bq1'], 'contains': ['11664.j1', '11664.m1', '11664.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 39957564, 1134499], 'label': '46656.ir.5832.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714948
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hm1', '1944.du1', '1944.ef1', '2916.f1', '2916.m1', '2916.z1', '2916.be1', '2916.bj1', '2916.bm1', '2916.bq1'], 'contains': ['11664.j1', '11664.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39917299, 39957120, 39957564], 'label': '46656.ir.5832.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714949
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '24.cf1'], 'contains': ['96.g1', '96.r1', '96.bi1', '144.bw1', '144.cl1', '144.co1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6267744007, 39366316080, 455255499150, 7, 325, 270715782960, 104], 'label': '46656.ir.48.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '48.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216714950
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fo1', '1944.dw1', '1944.fh1', '2916.e1', '2916.l1', '2916.bb1', '2916.bh1', '2916.bl1', '2916.bm1', '2916.bn1'], 'contains': ['11664.j1', '11664.bf1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 7, 1174320], 'label': '46656.ir.5832.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714951
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ho1', '1944.dx1', '1944.ej1', '2916.g1', '2916.o1', '2916.x1', '2916.bd1', '2916.bj1', '2916.bn1', '2916.br1'], 'contains': ['11664.j1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 1174320, 6227827818], 'label': '46656.ir.5832.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714952
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hp1', '1944.dy1', '1944.eg1', '2916.f1', '2916.n1', '2916.ba1', '2916.bf1', '2916.bk1', '2916.bn1', '2916.bp1'], 'contains': ['11664.j1', '11664.p1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 41051299, 39957564], 'label': '46656.ir.5832.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714953
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hq1', '1944.dz1', '1944.ek1', '2916.g1', '2916.p1', '2916.y1', '2916.bc1', '2916.bk1', '2916.bm1', '2916.bs1'], 'contains': ['11664.j1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 6267744618, 1174320], 'label': '46656.ir.5832.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714954
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.fs1', '648.hr1', '1944.ea1', '2916.h1', '2916.o1', '2916.z1', '2916.bf1', '2916.bg1', '2916.bl1', '2916.bs1'], 'contains': ['11664.j1', '11664.bm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [469, 6227464938, 1174320], 'label': '46656.ir.5832.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714955
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ft1', '648.hs1', '1944.eb1', '2916.h1', '2916.p1', '2916.ba1', '2916.be1', '2916.bh1', '2916.bi1', '2916.br1'], 'contains': ['11664.j1', '11664.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [469, 1174320, 6267381738], 'label': '46656.ir.5832.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714956
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.el1', '1944.em1', '1944.fi1', '2916.s1', '2916.bb1', '2916.bo1', '2916.bp1', '2916.bq1', '2916.br1', '2916.bs1'], 'contains': ['11664.j1', '11664.bc1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 41050800, 7], 'label': '46656.ir.5832.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '5832.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714957
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hu1', '1944.en1', '1944.er1', '1944.ev1', '1944.ex1', '1944.fb1', '2916.a1', '2916.v1', '2916.bc1'], 'contains': ['11664.k1', '11664.l1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 137, 7], 'label': '46656.ir.5832.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '5832.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714958
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hv1', '1944.eo1', '1944.es1', '1944.ey1', '2916.a1', '2916.w1', '2916.bd1'], 'contains': ['11664.k1', '11664.m1', '11664.n1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 6227827342, 7], 'label': '46656.ir.5832.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '5832.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714959
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hw1', '1944.ep1', '1944.et1', '1944.ew1', '1944.ez1', '1944.fc1', '2916.b1', '2916.v1', '2916.bd1'], 'contains': ['11664.k1', '11664.n1', '11664.o1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [6227388862, 6267744007, 7], 'label': '46656.ir.5832.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '5832.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.br1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714960
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '24.h1', '24.bd1', '24.bm1', '24.br1', '24.bs1', '24.ca1'], 'contains': ['96.a1', '144.cq1', '144.cy1', '144.cz1', '432.cx1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39917299, 39366316080, 7, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.48.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1', 'subgroup_fusion': None, 'weyl_group': '1728.47045'}
  • id: 216714961
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.hx1', '1944.eq1', '1944.eu1', '1944.fa1', '2916.b1', '2916.w1', '2916.bc1'], 'contains': ['11664.k1', '11664.p1', '11664.q1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [6267744007, 1174457, 7], 'label': '46656.ir.5832.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '5832.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714962
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.fj1', '1944.fk1', '1944.fl1', '1944.fw1', '2916.c1'], 'contains': ['11664.r1', '11664.s1', '11664.t1', '11664.w1', '11664.x1', '11664.bj1', '11664.bl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [41091120, 1174327, 6227827207], 'label': '46656.ir.5832.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '5832.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714963
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.fn1', '1944.fo1', '1944.fp1', '1944.fx1', '2916.c1', '2916.q1', '2916.bt1'], 'contains': ['11664.s1', '11664.u1', '11664.v1', '11664.z1', '11664.bd1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39916807, 1174320, 6227827200], 'label': '46656.ir.5832.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714964
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.iu1', '1944.fm1', '1944.fq1', '2916.i1', '2916.k1', '2916.bt1'], 'contains': ['11664.v1', '11664.ba1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [40327, 1174320, 6227827200], 'label': '46656.ir.5832.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714965
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.iv1', '1944.fr1', '1944.fs1', '1944.ft1', '2916.i1', '2916.q1', '2916.bb1'], 'contains': ['11664.v1', '11664.bc1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 1174320, 39957127], 'label': '46656.ir.5832.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714966
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.iw1', '1944.fu1', '1944.fv1', '1944.fy1', '2916.t1', '2916.bb1', '2916.bt1'], 'contains': ['11664.v1', '11664.bf1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 6227827200], 'label': '46656.ir.5832.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '5832.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714967
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ix1', '648.iy1', '1944.fz1', '2916.h1'], 'contains': ['11664.w1', '11664.bm1', '11664.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [41091120, 6267669018, 1174789], 'label': '46656.ir.5832.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.c1', 'old_label': '5832.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.by1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216714968
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.ga1', '1944.ge1', '1944.gv1', '2916.c1', '2916.r1', '2916.bu1'], 'contains': ['11664.y1', '11664.z1', '11664.bb1', '11664.bj1', '11664.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39916807, 1174320, 6227827207], 'label': '46656.ir.5832.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.bz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714969
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kk1', '1944.gb1', '1944.gd1', '2916.i1', '2916.l1', '2916.bu1'], 'contains': ['11664.y1', '11664.ba1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [40327, 6267381127, 1174320], 'label': '46656.ir.5832.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714970
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kl1', '1944.gc1', '1944.gf1', '2916.i1', '2916.r1', '2916.bo1'], 'contains': ['11664.y1', '11664.bc1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [1174320, 6227464327, 39957127], 'label': '46656.ir.5832.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714971
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1', '24.i1', '24.bc1', '24.be1', '24.bn1', '24.bu1', '24.ca1', '24.cb1'], 'contains': ['96.a1', '144.cr1', '144.cs1', '144.da1', '144.dg1', '432.cy1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 7, 6227827818, 325, 269279866800], 'label': '46656.ir.48.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216714972
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.km1', '1944.gi1', '1944.gk1', '1944.gm1', '2916.e1', '2916.q1', '2916.bu1'], 'contains': ['11664.z1', '11664.be1', '11664.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39916807, 6267381127, 1174320], 'label': '46656.ir.5832.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.cc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714973
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kn1', '1944.gj1', '1944.gl1', '2916.e1', '2916.r1', '2916.bt1'], 'contains': ['11664.z1', '11664.bf1', '11664.bg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39916807, 6267381120, 1174320], 'label': '46656.ir.5832.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.cd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714974
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ko1', '1944.gg1', '1944.gn1', '2916.j1', '2916.k1', '2916.bu1'], 'contains': ['11664.ba1', '11664.bb1', '11664.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [40327, 1174320, 6227827207], 'label': '46656.ir.5832.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '5832.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714975
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kp1', '1944.gh1', '1944.go1', '2916.j1', '2916.l1', '2916.bt1'], 'contains': ['11664.ba1', '11664.bd1', '11664.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381120, 40327, 1174320], 'label': '46656.ir.5832.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.cf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714976
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kq1', '1944.gp1', '1944.gq1', '2916.j1', '2916.r1', '2916.bb1'], 'contains': ['11664.bb1', '11664.bc1', '11664.bf1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [1174320, 6227827207, 39957127], 'label': '46656.ir.5832.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.cg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714977
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kr1', '1944.gr1', '1944.gs1', '1944.gt1', '2916.j1', '2916.q1', '2916.bo1'], 'contains': ['11664.bc1', '11664.bd1', '11664.be1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 1174320, 39957127], 'label': '46656.ir.5832.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.ch1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714978
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ks1', '1944.gu1', '1944.gw1', '1944.hf1', '2916.t1', '2916.bo1', '2916.bu1'], 'contains': ['11664.y1', '11664.be1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 41050800, 6267744000], 'label': '46656.ir.5832.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '5832.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.ci1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714979
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.gx1', '1944.gy1', '1944.hg1', '2916.s1', '2916.bt1', '2916.bu1'], 'contains': ['11664.z1', '11664.ba1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 39957120, 41050800], 'label': '46656.ir.5832.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '5832.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714980
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.ku1', '1944.gz1', '1944.ha1', '1944.hb1', '1944.hh1', '2916.u1', '2916.bb1', '2916.bu1'], 'contains': ['11664.bb1', '11664.bh1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 41050800, 6227827207], 'label': '46656.ir.5832.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.ck1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714981
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '5832.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.kv1', '1944.hc1', '1944.hd1', '1944.he1', '1944.hi1', '2916.u1', '2916.bo1', '2916.bt1'], 'contains': ['11664.bd1', '11664.bg1', '11664.bi1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 39957120, 41050800], 'label': '46656.ir.5832.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '5832.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.cl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 216714982
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '24.j1', '24.be1', '24.bm1', '24.bp1', '24.bv1', '24.cc1'], 'contains': ['96.a1', '144.cu1', '144.dc1', '144.dd1', '432.da1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 269279866800, 39957619], 'label': '46656.ir.48.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216714983
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.b1', '2592.c1', '2592.d1', '2592.e1', '2592.f1', '2592.k1', '3888.c1', '3888.d1', '3888.h1', '3888.l1', '3888.p1', '3888.s1', '3888.x1'], 'contains': ['15552.a1', '23328.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916800, 104], 'label': '46656.ir.7776.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '7776.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714984
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.b1', '2592.g1', '2592.h1', '2592.o1', '3888.a1', '3888.i1', '3888.k1', '3888.m1', '3888.t1', '3888.y1', '3888.bg1'], 'contains': ['15552.b1', '23328.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916800, 37885034880], 'label': '46656.ir.7776.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '7776.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714985
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.c1', '2592.h1', '2592.i1', '2592.l1', '3888.b1', '3888.e1', '3888.g1', '3888.j1', '3888.o1', '3888.q1', '3888.u1'], 'contains': ['15552.d1', '23328.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39916800], 'label': '46656.ir.7776.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '7776.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714986
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.b1', '2592.d1', '2592.g1', '2592.i1', '2592.j1', '2592.j2', '2592.m1', '3888.n1', '3888.v1', '3888.z1'], 'contains': ['15552.e1', '23328.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684835, 39916800], 'label': '46656.ir.7776.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.br1', 'old_label': '7776.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714987
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.c1', '2592.e1', '2592.g1', '2592.i1', '2592.j1', '2592.j2', '2592.n1', '3888.f1', '3888.r1', '3888.w1'], 'contains': ['15552.g1', '23328.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39916800, 40323593955], 'label': '46656.ir.7776.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.j1', 'old_label': '7776.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714988
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.k1', '2592.l1', '2592.m1', '2592.n1', '2592.o1', '3888.ba1', '3888.bb1', '3888.bc1', '3888.bd1', '3888.be1', '3888.bf1', '3888.bg1'], 'contains': ['15552.b1', '23328.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 39916800], 'label': '46656.ir.7776.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '7776.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714989
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.t1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.p1', '2592.q1', '2592.u1', '3888.a1', '3888.ba1', '3888.bh1', '3888.bn1', '3888.bq1', '3888.br1', '3888.bu1', '3888.by1', '3888.bz1', '3888.ca1', '3888.cb1', '3888.cc1', '3888.cd1', '3888.ce1', '3888.cf1'], 'contains': ['15552.b1', '23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 37885034880], 'label': '46656.ir.7776.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '7776.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714990
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.cl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.p1', '2592.r1', '2592.s1', '2592.t1', '2592.v1', '3888.bi1', '3888.bo1', '3888.bv1', '3888.cg1', '3888.ch1', '3888.ci1', '3888.cj1'], 'contains': ['15552.c1', '23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [301891126320, 7], 'label': '46656.ir.7776.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '7776.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714991
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.p1', '2592.q1', '2592.r1', '2592.w1', '3888.b1', '3888.bj1', '3888.bk1', '3888.bp1', '3888.bs1', '3888.bt1', '3888.bw1', '3888.ck1', '3888.cl1', '3888.cm1', '3888.cn1', '3888.co1', '3888.cp1', '3888.cq1', '3888.cr1'], 'contains': ['15552.d1', '23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 7], 'label': '46656.ir.7776.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '7776.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714992
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.eo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.el1', '2592.s1', '2592.x1', '3888.bl1', '3888.bm1', '3888.bx1', '3888.cs1', '3888.ct1', '3888.cu1', '3888.cv1'], 'contains': ['15552.h1', '23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [7, 655477406640], 'label': '46656.ir.7776.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '7776.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714993
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '3.a1'], 'contains': ['12.b1', '12.bl1', '12.bo1', '12.bp1', '12.bt1', '12.bx1', '12.bz1', '18.w1', '54.bd1', '54.bl1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 499, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.6.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216714994
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '24.i1', '24.bd1', '24.bf1', '24.bn1', '24.bw1', '24.bz1', '24.cc1'], 'contains': ['96.a1', '144.cv1', '144.cw1', '144.de1', '144.di1', '432.db1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6267744618, 7, 325, 269279866800], 'label': '46656.ir.48.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216714995
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.a1', '2592.u1', '2592.v1', '2592.w1', '2592.x1', '3888.c1', '3888.cw1', '3888.cx1', '3888.cy1', '3888.cz1'], 'contains': ['15552.a1', '23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [7, 435], 'label': '46656.ir.7776.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2592.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '7776.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216714996
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.bi1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.y1', '2592.z1', '2592.ba1', '2592.bb1', '2592.bc1', '2592.bd1', '2592.be1', '2592.bk1', '2592.bl1', '3888.d1', '3888.cw1', '3888.da1', '3888.df1', '3888.dj1', '3888.dm1', '3888.dt1'], 'contains': ['15552.a1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6227827200, 104], 'label': '46656.ir.7776.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1', 'old_label': '7776.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714997
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.cn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.y1', '2592.bf1', '2592.bg1', '2592.bm1', '3888.bb1', '3888.bh1', '3888.db1', '3888.dg1', '3888.di1', '3888.dn1', '3888.du1'], 'contains': ['15552.b1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 6227827200], 'label': '46656.ir.7776.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '7776.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714998
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.z1', '2592.bf1', '2592.bh1', '2592.bo1', '2592.bp1', '3888.bi1', '3888.dc1', '3888.do1'], 'contains': ['15552.c1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [387999647280, 6227827200], 'label': '46656.ir.7776.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cf1', 'old_label': '7776.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216714999
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ba1', '2592.bf1', '2592.bi1', '2592.bn1', '3888.e1', '3888.bj1', '3888.dd1', '3888.de1', '3888.dk1', '3888.dp1', '3888.ec1'], 'contains': ['15552.d1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 6227827200], 'label': '46656.ir.7776.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '7776.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715000
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.eo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.y1', '2592.bb1', '2592.bh1', '2592.bi1', '2592.bj1', '2592.bj2', '2592.bq1', '3888.dh1', '3888.dq1', '3888.dv1'], 'contains': ['15552.e1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280813235, 6227827200], 'label': '46656.ir.7776.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fy1', 'old_label': '7776.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715001
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.z1', '2592.bc1', '2592.bg1', '2592.bh1', '2592.bi1', '2592.bj1', '2592.bj2', '2592.bs1', '2592.bt1', '3888.dr1'], 'contains': ['15552.f1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6227827200, 295664181555], 'label': '46656.ir.7776.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ds1', 'old_label': '7776.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715002
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ba1', '2592.bd1', '2592.bg1', '2592.bh1', '2592.bj1', '2592.bj2', '2592.br1', '3888.f1', '3888.dl1', '3888.ds1'], 'contains': ['15552.g1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316515, 6227827200], 'label': '46656.ir.7776.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.be1', 'old_label': '7776.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715003
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.bk1', '2592.bm1', '2592.bn1', '2592.bo1', '2592.bq1', '2592.br1', '2592.bs1', '3888.g1', '3888.bk1', '3888.dx1', '3888.dy1', '3888.dz1', '3888.eb1', '3888.ec1'], 'contains': ['15552.d1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593520, 6227827200], 'label': '46656.ir.7776.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '7776.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715004
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.fy1', '2592.bl1', '2592.bp1', '2592.bt1', '3888.bl1', '3888.dw1', '3888.ea1'], 'contains': ['15552.h1', '23328.c1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [624302466480, 6227827200], 'label': '46656.ir.7776.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '7776.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715005
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.bi1', '24.bk1', '24.cd1'], 'contains': ['96.f1', '144.df1', '144.dj1', '432.dc1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [40323593624, 499, 7, 325, 270715782960, 40323593520, 461482882830], 'label': '46656.ir.48.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '48.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715006
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.bu1', '2592.bv1', '2592.bw1', '2592.bx1', '2592.by1', '2592.bz1', '3888.h1', '3888.cx1', '3888.da1', '3888.ed1', '3888.ee1'], 'contains': ['15552.a1', '23328.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 104], 'label': '46656.ir.7776.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.l1', 'old_label': '7776.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715007
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.by1', '2592.bu1', '2592.ca1', '3888.bm1', '3888.dw1', '3888.ef1'], 'contains': ['15552.h1', '23328.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 93576273840], 'label': '46656.ir.7776.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '7776.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715008
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.by1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.bz1', '2592.bu1', '2592.bv1', '2592.cb1', '3888.eg1'], 'contains': ['15552.i1', '23328.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 864, 'diagramx': None, 'generators': [41091120, 174451657344], 'label': '46656.ir.7776.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.hz1', 'old_label': '7776.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715009
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.bx1', '2592.cc1', '2592.cd1', '3888.i1', '3888.bc1', '3888.bn1', '3888.db1', '3888.eh1', '3888.ej1', '3888.ek1'], 'contains': ['15552.b1', '23328.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120, 37885034880], 'label': '46656.ir.7776.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '7776.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715010
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.gd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.by1', '2592.ca1', '2592.cb1', '2592.cc1', '2592.ce1', '3888.bo1', '3888.dc1', '3888.el1'], 'contains': ['15552.c1', '23328.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 301891126320], 'label': '46656.ir.7776.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '7776.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715011
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.bz1', '2592.cc1', '2592.cd1', '2592.ce1', '3888.j1', '3888.bp1', '3888.dd1', '3888.dx1', '3888.ei1', '3888.em1', '3888.en1'], 'contains': ['15552.d1', '23328.d1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080], 'label': '46656.ir.7776.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '7776.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715012
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cf1', '2592.cg1', '2592.ch1', '2592.ci1', '2592.cj1', '3888.h1', '3888.x1', '3888.cy1', '3888.dt1', '3888.eo1', '3888.er1', '3888.eu1', '3888.ew1', '3888.ex1', '3888.fa1', '3888.fd1', '3888.fe1', '3888.ff1', '3888.fg1', '3888.fu1'], 'contains': ['15552.a1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39957120, 39957224], 'label': '46656.ir.7776.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.q1', 'old_label': '7776.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715013
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cf1', '2592.ck1', '2592.cm1', '3888.y1', '3888.bc1', '3888.bq1', '3888.du1', '3888.ep1', '3888.eq1', '3888.es1', '3888.ev1', '3888.ey1', '3888.fb1', '3888.fh1', '3888.fi1', '3888.fj1', '3888.fk1', '3888.fx1'], 'contains': ['15552.b1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 1481684400], 'label': '46656.ir.7776.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '7776.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715014
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.bc1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cf1', '2592.cg1', '2592.cl1', '2592.cn1', '3888.z1', '3888.dv1', '3888.et1', '3888.ez1', '3888.fc1', '3888.fl1', '3888.fm1'], 'contains': ['15552.e1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39957120, 1521641624], 'label': '46656.ir.7776.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.t1', 'old_label': '7776.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715015
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.bt1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ci1', '2592.cl1', '2592.cm1', '2592.co1', '3888.i1', '3888.bg1', '3888.br1', '3888.fo1', '3888.fq1', '3888.fs1', '3888.fx1'], 'contains': ['15552.b1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 37885034880], 'label': '46656.ir.7776.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '7776.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715016
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1', '24.bi1', '24.bl1', '24.ce1'], 'contains': ['96.f1', '144.dg1', '144.dk1', '432.dd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [40323593624, 7, 325, 270715782960, 6227827818, 40323593520, 461482882830], 'label': '46656.ir.48.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '48.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715017
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cj1', '2592.ck1', '2592.cn1', '2592.co1', '3888.j1', '3888.bs1', '3888.ec1', '3888.fn1', '3888.fp1', '3888.fr1', '3888.ft1'], 'contains': ['15552.d1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [387037284480, 39957120], 'label': '46656.ir.7776.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '7776.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715018
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cp1', '2592.cq1', '2592.cr1', '2592.cs1', '2592.ct1', '2592.cu1', '2592.cv1', '3888.d1', '3888.cz1', '3888.da1', '3888.eo1', '3888.fz1', '3888.ga1', '3888.gd1'], 'contains': ['15552.a1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6267744000, 435], 'label': '46656.ir.7776.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.g1', 'old_label': '7776.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715019
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cp1', '2592.cw1', '2592.cy1', '2592.cz1', '3888.e1', '3888.bt1', '3888.dx1', '3888.fn1', '3888.fy1', '3888.gb1', '3888.ge1'], 'contains': ['15552.d1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 6267744000], 'label': '46656.ir.7776.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '7776.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715020
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.cp1', '2592.cq1', '2592.cx1', '2592.da1', '2592.db1', '3888.f1', '3888.gc1', '3888.gf1'], 'contains': ['15552.g1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [39366316515, 6267744000], 'label': '46656.ir.7776.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.p1', 'old_label': '7776.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715021
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.ef1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cs1', '2592.cw1', '2592.cx1', '2592.dc1', '3888.bb1', '3888.bu1', '3888.db1', '3888.ep1', '3888.gh1', '3888.gi1', '3888.gm1'], 'contains': ['15552.b1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 6267744000], 'label': '46656.ir.7776.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '7776.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715022
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.fz1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ct1', '2592.cz1', '2592.da1', '2592.dc1', '2592.dd1', '2592.de1', '3888.bv1', '3888.dc1', '3888.gj1'], 'contains': ['15552.c1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [301891126320, 6267744000], 'label': '46656.ir.7776.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '7776.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715023
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.cu1', '2592.cy1', '2592.db1', '2592.dc1', '3888.g1', '3888.bw1', '3888.dd1', '3888.fn1', '3888.gg1', '3888.gk1', '3888.gn1'], 'contains': ['15552.d1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593520, 6267744000], 'label': '46656.ir.7776.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '7776.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715024
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.hf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.gw1', '2592.cv1', '2592.dd1', '3888.bx1', '3888.dw1', '3888.gl1'], 'contains': ['15552.h1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [655477406640, 6267744000], 'label': '46656.ir.7776.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '7776.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715025
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.df1', '2592.dg1', '2592.dj1', '2592.dk1', '3888.a1', '3888.k1', '3888.bd1', '3888.eh1', '3888.eq1', '3888.fo1', '3888.fq1'], 'contains': ['15552.b1', '23328.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 37885034880], 'label': '46656.ir.7776.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '7776.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bm1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715026
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.df1', '2592.dh1', '2592.di1', '2592.dl1', '3888.b1', '3888.de1', '3888.dy1', '3888.ei1', '3888.fp1', '3888.fy1', '3888.gg1'], 'contains': ['15552.d1', '23328.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39916807, 39366316080], 'label': '46656.ir.7776.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '7776.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715027
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '24.bj1', '24.bk1', '24.ce1'], 'contains': ['96.f1', '144.dh1', '144.dl1', '432.de1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091619, 7, 325, 270715782960, 40323593520, 461482882830], 'label': '46656.ir.48.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715028
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.cq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.dg1', '2592.dh1', '2592.dm1', '2592.dn1', '2592.do1', '3888.c1', '3888.l1', '3888.df1', '3888.ed1', '3888.er1', '3888.eu1', '3888.fz1'], 'contains': ['15552.a1', '23328.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 435], 'label': '46656.ir.7776.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '7776.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715029
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.di1', '2592.dk1', '2592.dm1', '3888.m1', '3888.ba1', '3888.dg1', '3888.ej1', '3888.es1', '3888.fq1', '3888.gh1'], 'contains': ['15552.b1', '23328.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 268280812800], 'label': '46656.ir.7776.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '7776.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715030
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.dl1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.dj1', '2592.dl1', '2592.dm1', '2592.dn1', '3888.n1', '3888.dh1', '3888.et1'], 'contains': ['15552.e1', '23328.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39916807, 268280813235], 'label': '46656.ir.7776.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '7776.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715031
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.da1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.dp1', '2592.dq1', '2592.dt1', '2592.du1', '3888.be1', '3888.bh1', '3888.di1', '3888.ek1', '3888.ev1', '3888.gh1', '3888.gi1'], 'contains': ['15552.b1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [268280812800, 6227827207], 'label': '46656.ir.7776.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '7776.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715032
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.ds1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.dp1', '2592.dr1', '2592.dw1', '2592.dx1', '2592.dy1', '2592.dz1', '3888.bi1', '3888.el1', '3888.gj1'], 'contains': ['15552.c1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [387999647280, 6227827207], 'label': '46656.ir.7776.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cs1', 'old_label': '7776.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715033
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bi1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.dp1', '2592.ds1', '2592.dv1', '2592.ea1', '3888.o1', '3888.bj1', '3888.dz1', '3888.em1', '3888.fr1', '3888.fy1', '3888.gk1'], 'contains': ['15552.d1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39366316080, 6227827207], 'label': '46656.ir.7776.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '7776.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715034
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.cu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.dq1', '2592.dr1', '2592.ds1', '2592.eb1', '2592.ec1', '2592.ed1', '2592.ee1', '2592.ef1', '3888.p1', '3888.cw1', '3888.dj1', '3888.ee1', '3888.ew1', '3888.fz1', '3888.ga1'], 'contains': ['15552.a1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [6227827207, 435], 'label': '46656.ir.7776.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '7776.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715035
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.dt1', '2592.dv1', '2592.dw1', '2592.eb1', '3888.q1', '3888.bk1', '3888.dk1', '3888.en1', '3888.fr1', '3888.gb1', '3888.gg1'], 'contains': ['15552.d1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593520, 6227827207], 'label': '46656.ir.7776.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '7776.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715036
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.bt1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.du1', '2592.dx1', '2592.ea1', '2592.eb1', '2592.ec1', '3888.r1', '3888.dl1', '3888.gc1'], 'contains': ['15552.g1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [40323593955, 6227827207], 'label': '46656.ir.7776.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.cc1', 'old_label': '7776.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715037
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dl1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.ha1', '2592.dy1', '2592.ed1', '3888.bl1', '3888.ef1', '3888.gl1'], 'contains': ['15552.h1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [624302466480, 6227827207], 'label': '46656.ir.7776.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '7776.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715038
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '24.bj1', '24.bl1', '24.cd1'], 'contains': ['96.f1', '144.di1', '144.dm1', '432.df1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 6267744618, 7, 325, 270715782960, 104, 716634334350], 'label': '46656.ir.48.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715039
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.y1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.hb1', '2592.dz1', '2592.ed1', '2592.ee1', '3888.eg1'], 'contains': ['15552.i1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [722937882588, 6227827207], 'label': '46656.ir.7776.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hz1', 'old_label': '7776.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.by1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715040
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.eg1', '2592.eh1', '2592.ei1', '2592.ej1', '2592.ek1', '3888.k1', '3888.bf1', '3888.bq1', '3888.di1', '3888.ej1', '3888.fs1', '3888.gm1', '3888.go1', '3888.gp1'], 'contains': ['15552.b1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [1481684400, 39957127], 'label': '46656.ir.7776.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '7776.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.bz1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715041
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bu1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.eg1', '2592.el1', '2592.em1', '2592.en1', '2592.eo1', '2592.ep1', '3888.l1', '3888.s1', '3888.cy1', '3888.dj1', '3888.ed1', '3888.ex1', '3888.gd1'], 'contains': ['15552.a1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [39957127, 435], 'label': '46656.ir.7776.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.r1', 'old_label': '7776.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ca1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715042
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.br1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ek1', '2592.el1', '2592.eq1', '2592.er1', '3888.m1', '3888.t1', '3888.bd1', '3888.br1', '3888.eh1', '3888.ey1', '3888.fs1'], 'contains': ['15552.b1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [39957127, 37885034880], 'label': '46656.ir.7776.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.x1', 'old_label': '7776.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715043
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.eh1', '2592.em1', '2592.er1', '2592.es1', '3888.u1', '3888.bs1', '3888.dk1', '3888.dz1', '3888.ei1', '3888.ge1', '3888.gn1'], 'contains': ['15552.d1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [387037284480, 39957127], 'label': '46656.ir.7776.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '7776.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715044
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ei1', '2592.el1', '2592.en1', '2592.eq1', '2592.es1', '2592.et1', '2592.et2', '3888.n1', '3888.v1', '3888.ez1'], 'contains': ['15552.e1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [37885034984, 39957127], 'label': '46656.ir.7776.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.dh1', 'old_label': '7776.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715045
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ej1', '2592.em1', '2592.eo1', '2592.eq1', '2592.es1', '2592.et1', '2592.et2', '3888.w1', '3888.dl1', '3888.gf1'], 'contains': ['15552.g1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [293708217704, 39957127], 'label': '46656.ir.7776.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.cr1', 'old_label': '7776.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ce1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715046
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.df1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.gx1', '2592.eu1', '2592.ev1', '2592.ew1', '3888.bm1', '3888.ea1', '3888.gl1'], 'contains': ['15552.h1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [93576273840, 41091127], 'label': '46656.ir.7776.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '7776.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715047
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.bm1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.eu1', '2592.ex1', '2592.ey1', '2592.ez1', '2592.fa1', '2592.fb1', '2592.fc1', '2592.fd1', '3888.s1', '3888.cx1', '3888.dm1', '3888.er1', '3888.ga1'], 'contains': ['15552.a1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [41091127, 435], 'label': '46656.ir.7776.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.n1', 'old_label': '7776.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715048
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ex1', '2592.fe1', '2592.ff1', '2592.fg1', '2592.fh1', '3888.t1', '3888.bf1', '3888.bn1', '3888.dn1', '3888.es1', '3888.fo1', '3888.gi1'], 'contains': ['15552.b1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [37885034880, 41091127], 'label': '46656.ir.7776.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '7776.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ch1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715049
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '24.cf1'], 'contains': ['96.g1', '144.df1', '144.dn1', '432.dg1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [40323593624, 195088320270, 499, 7, 325, 270715782960, 40323593520], 'label': '46656.ir.48.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '48.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1', 'subgroup_fusion': None, 'weyl_group': '1944.3491'}
  • id: 216715050
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ev1', '2592.ey1', '2592.fe1', '2592.fi1', '2592.fj1', '2592.fk1', '3888.bo1', '3888.do1', '3888.gj1'], 'contains': ['15552.c1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [301891126320, 41091127], 'label': '46656.ir.7776.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cu1', 'old_label': '7776.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715051
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ez1', '2592.fe1', '2592.fh1', '2592.fi1', '2592.fl1', '2592.fm1', '2592.fn1', '3888.u1', '3888.bp1', '3888.dp1', '3888.eb1', '3888.fp1', '3888.gb1', '3888.gk1'], 'contains': ['15552.d1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39366316080, 41091127], 'label': '46656.ir.7776.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '7776.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715052
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ex1', '2592.fa1', '2592.ff1', '2592.fj1', '2592.fl1', '2592.fm1', '2592.fo1', '2592.fo2', '2592.fp1', '2592.fp2', '3888.v1', '3888.dq1', '3888.et1'], 'contains': ['15552.e1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': None, 'generators': [1481684835, 41091127], 'label': '46656.ir.7776.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.x1', 'old_label': '7776.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ck1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715053
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ew1', '2592.ey1', '2592.fb1', '2592.fg1', '2592.fj1', '2592.fl1', '2592.fn1', '2592.fo1', '2592.fo2', '2592.fq1', '3888.dr1'], 'contains': ['15552.f1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [294706904115, 41091127], 'label': '46656.ir.7776.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hc1', 'old_label': '7776.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715054
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.ez1', '2592.fc1', '2592.ff1', '2592.fg1', '2592.fj1', '2592.fk1', '2592.fm1', '2592.fn1', '2592.fo1', '2592.fo2', '2592.fp1', '2592.fp2', '2592.fq1', '3888.w1', '3888.ds1', '3888.gc1'], 'contains': ['15552.g1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': None, 'generators': [40323593624, 41091127], 'label': '46656.ir.7776.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1944.q1', 'old_label': '7776.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715055
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.fr1', '2592.fs1', '2592.ft1', '2592.fu1', '2592.fv1', '2592.fw1', '2592.fx1', '3888.o1', '3888.bt1', '3888.de1', '3888.eb1', '3888.en1', '3888.ft1', '3888.gn1'], 'contains': ['15552.d1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 39366316080], 'label': '46656.ir.7776.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '7776.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715056
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.fr1', '2592.fy1', '2592.fz1', '2592.ga1', '2592.gb1', '2592.gc1', '2592.gd1', '2592.ge1', '2592.gf1', '2592.gg1', '3888.p1', '3888.cz1', '3888.df1', '3888.dm1', '3888.ee1', '3888.fa1', '3888.gd1'], 'contains': ['15552.a1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [6267744007, 435], 'label': '46656.ir.7776.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '7776.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.co1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715057
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.cj1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.fs1', '2592.fy1', '2592.gh1', '2592.gi1', '3888.be1', '3888.bu1', '3888.dg1', '3888.dn1', '3888.ek1', '3888.fb1', '3888.gm1'], 'contains': ['15552.b1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 268280812800], 'label': '46656.ir.7776.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '7776.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715058
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.cy1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.fu1', '2592.fz1', '2592.gh1', '2592.gj1', '2592.gk1', '2592.gl1', '2592.gm1', '2592.gn1', '3888.bv1', '3888.do1', '3888.el1'], 'contains': ['15552.c1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [6267744007, 301891126320], 'label': '46656.ir.7776.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.cz1', 'old_label': '7776.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715059
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.ft1', '2592.ga1', '2592.gh1', '2592.go1', '3888.q1', '3888.bw1', '3888.dp1', '3888.dy1', '3888.em1', '3888.ft1', '3888.ge1'], 'contains': ['15552.d1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6267744007, 40323593520], 'label': '46656.ir.7776.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '7776.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715060
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '24.cf1'], 'contains': ['96.g1', '144.di1', '144.do1', '432.dh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 455255499150, 6267744618, 7, 325, 270715782960, 104], 'label': '46656.ir.48.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '48.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216715061
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.fv1', '2592.fy1', '2592.gb1', '2592.gj1', '2592.go1', '2592.gp1', '2592.gp2', '3888.dh1', '3888.dq1', '3888.fc1'], 'contains': ['15552.e1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [6267744007, 268280812904], 'label': '46656.ir.7776.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.ir1', 'old_label': '7776.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715062
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.fx1', '2592.fz1', '2592.gc1', '2592.gi1', '2592.gj1', '2592.go1', '2592.gp1', '2592.gp2', '2592.gq1', '2592.gr1', '3888.dr1'], 'contains': ['15552.f1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': None, 'generators': [6267744007, 294706904115], 'label': '46656.ir.7776.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1296.hj1', 'old_label': '7776.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.ct1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715063
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2592.fw1', '2592.ga1', '2592.gd1', '2592.gi1', '2592.gj1', '2592.gp1', '2592.gp2', '3888.r1', '3888.ds1', '3888.gf1'], 'contains': ['15552.g1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': None, 'generators': [40323593624, 6267744007], 'label': '46656.ir.7776.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.w1', 'old_label': '7776.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715064
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.hd1', '2592.ge1', '2592.gk1', '2592.gq1', '3888.bx1', '3888.ea1', '3888.ef1'], 'contains': ['15552.h1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 972, 'diagramx': None, 'generators': [6267744007, 655477406640], 'label': '46656.ir.7776.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '972.cg1', 'old_label': '7776.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715065
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '7776.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1944.he1', '2592.ge1', '2592.gf1', '2592.gl1', '2592.gq1', '2592.gr1', '3888.eg1'], 'contains': ['15552.i1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 7776, 'diagramx': None, 'generators': [6267744007, 462811064028], 'label': '46656.ir.7776.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3888.eg1', 'old_label': '7776.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7776.cw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715066
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.a1', '3888.b1', '3888.c1', '3888.ba1', '5832.a1', '5832.b1', '5832.c1', '5832.d1', '5832.e1', '5832.f1', '5832.n1'], 'contains': ['23328.a1', '23328.b1', '23328.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [7, 39916800], 'label': '46656.ir.11664.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '11664.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715067
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.d1', '3888.e1', '3888.f1', '3888.g1', '3888.bb1', '5832.a1', '5832.g1', '5832.h1'], 'contains': ['23328.a1', '23328.c1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39916800, 6227827200], 'label': '46656.ir.11664.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '11664.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715068
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.h1', '3888.i1', '3888.j1', '3888.bc1', '5832.b1', '5832.h1', '5832.i1', '5832.j1', '5832.k1', '5832.l1', '5832.t1'], 'contains': ['23328.a1', '23328.d1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957120, 1134000], 'label': '46656.ir.11664.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '11664.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715069
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.k1', '3888.l1', '3888.m1', '3888.n1', '3888.bd1', '5832.i1', '5832.n1', '5832.q1'], 'contains': ['23328.a1', '23328.g1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916800, 39957127], 'label': '46656.ir.11664.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.o1', 'old_label': '11664.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715070
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.o1', '3888.p1', '3888.q1', '3888.r1', '3888.be1', '5832.a1', '5832.g1', '5832.j1'], 'contains': ['23328.a1', '23328.h1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916800, 6227827207], 'label': '46656.ir.11664.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '11664.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715071
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1', '24.l1', '24.bb1', '24.cg1'], 'contains': ['96.b1', '96.h1', '96.p1', '144.dp1', '144.du1', '144.dv1', '144.dw1', '144.dx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827200], 'label': '46656.ir.48.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1', 'subgroup_fusion': None, 'weyl_group': '864.4367'}
  • id: 216715072
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.s1', '3888.t1', '3888.u1', '3888.v1', '3888.w1', '3888.bf1', '5832.b1', '5832.g1', '5832.m1', '5832.q1'], 'contains': ['23328.a1', '23328.i1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [1134000, 39957127], 'label': '46656.ir.11664.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '11664.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715073
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.x1', '3888.y1', '3888.z1', '3888.bg1', '5832.n1', '5832.o1', '5832.p1', '5832.q1', '5832.r1', '5832.s1', '5832.t1'], 'contains': ['23328.a1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 39916800], 'label': '46656.ir.11664.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '11664.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715074
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.bh1', '3888.bi1', '3888.bj1', '3888.bk1', '3888.bl1', '3888.cw1', '5832.a1', '5832.u1', '5832.v1', '5832.w1', '5832.x1', '5832.y1', '5832.z1'], 'contains': ['23328.b1', '23328.c1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [7, 6227827207], 'label': '46656.ir.11664.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '11664.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715075
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.bm1', '3888.bn1', '3888.bo1', '3888.bp1', '3888.cx1', '5832.b1', '5832.u1', '5832.ba1', '5832.bb1', '5832.bc1'], 'contains': ['23328.b1', '23328.d1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41091120, 7], 'label': '46656.ir.11664.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '11664.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715076
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.bq1', '3888.br1', '3888.bs1', '3888.cy1', '5832.b1', '5832.n1', '5832.z1', '5832.bd1', '5832.be1', '5832.bf1', '5832.bg1', '5832.bh1', '5832.bi1', '5832.bj1', '5832.bk1', '5832.bl1', '5832.bm1', '5832.bn1', '5832.bo1'], 'contains': ['23328.b1', '23328.e1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957120, 7], 'label': '46656.ir.11664.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '11664.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715077
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.bt1', '3888.bu1', '3888.bv1', '3888.bw1', '3888.bx1', '3888.cz1', '5832.a1', '5832.u1', '5832.bd1', '5832.bp1', '5832.bq1', '5832.br1', '5832.bs1'], 'contains': ['23328.b1', '23328.f1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007, 7], 'label': '46656.ir.11664.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '11664.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715078
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1', '3888.by1', '3888.cg1', '3888.ck1', '3888.cs1', '5832.c1', '5832.v1', '5832.ba1', '5832.be1', '5832.bp1'], 'contains': ['23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [499, 444], 'label': '46656.ir.11664.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1296.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '11664.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715079
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fb1', '3888.bz1', '3888.ca1', '3888.cl1', '5832.c1', '5832.d1', '5832.w1', '5832.bb1', '5832.bg1', '5832.bh1', '5832.bq1'], 'contains': ['23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39917299, 444], 'label': '46656.ir.11664.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '11664.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715080
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fc1', '3888.cb1', '3888.ch1', '3888.cm1', '3888.cn1', '3888.ct1', '5832.e1', '5832.v1', '5832.x1', '5832.bc1', '5832.bj1', '5832.bq1', '5832.br1'], 'contains': ['23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [469, 6227827818], 'label': '46656.ir.11664.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '11664.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715081
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fd1', '3888.cc1', '3888.ci1', '3888.co1', '3888.cu1', '5832.f1', '5832.y1', '5832.ba1', '5832.bg1', '5832.br1'], 'contains': ['23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41091619, 444], 'label': '46656.ir.11664.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '11664.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715082
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.cg1', '24.ch1'], 'contains': ['96.h1', '96.t1', '96.bg1', '144.dq1', '144.dy1', '144.dz1', '144.ea1', '144.eb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827200], 'label': '46656.ir.48.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216715083
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.fe1', '3888.cd1', '3888.ce1', '3888.cp1', '5832.d1', '5832.f1', '5832.x1', '5832.bb1', '5832.be1', '5832.bk1', '5832.bs1'], 'contains': ['23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [444, 39957619], 'label': '46656.ir.11664.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '11664.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715084
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.ff1', '3888.cf1', '3888.cj1', '3888.cq1', '3888.cr1', '3888.cv1', '5832.e1', '5832.w1', '5832.y1', '5832.bc1', '5832.bl1', '5832.bp1', '5832.bs1'], 'contains': ['23328.b1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [469, 6267744618], 'label': '46656.ir.11664.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '11664.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715085
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.da1', '3888.db1', '3888.dc1', '3888.dd1', '3888.dw1', '3888.dx1', '5832.h1', '5832.u1', '5832.bt1'], 'contains': ['23328.c1', '23328.d1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [41091120, 6227827200], 'label': '46656.ir.11664.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.e1', 'old_label': '11664.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715086
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.de1', '3888.df1', '3888.dg1', '3888.dh1', '3888.dy1', '5832.a1', '5832.bt1', '5832.bu1'], 'contains': ['23328.c1', '23328.g1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916807, 6227827200], 'label': '46656.ir.11664.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '11664.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715087
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.di1', '3888.dj1', '3888.dk1', '3888.dl1', '3888.dz1', '5832.g1', '5832.z1', '5832.bt1'], 'contains': ['23328.c1', '23328.h1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1174327, 6227827207], 'label': '46656.ir.11664.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.f1', 'old_label': '11664.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715088
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.dm1', '3888.dn1', '3888.do1', '3888.dp1', '3888.dq1', '3888.dr1', '3888.ds1', '3888.ea1', '3888.eb1', '5832.g1', '5832.u1', '5832.bu1'], 'contains': ['23328.c1', '23328.j1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [6227827200, 41091127], 'label': '46656.ir.11664.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '11664.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715089
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.dt1', '3888.du1', '3888.dv1', '3888.ec1', '5832.h1', '5832.o1', '5832.z1', '5832.bu1', '5832.bv1', '5832.bw1', '5832.bx1'], 'contains': ['23328.c1', '23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1174320, 6227827200], 'label': '46656.ir.11664.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '11664.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715090
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.ed1', '3888.eh1', '3888.ei1', '3888.ej1', '5832.b1', '5832.i1', '5832.bt1', '5832.by1'], 'contains': ['23328.d1', '23328.g1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [41091120, 39957127], 'label': '46656.ir.11664.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '11664.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715091
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.ee1', '3888.ef1', '3888.eg1', '3888.ek1', '3888.el1', '3888.em1', '3888.en1', '5832.j1', '5832.u1', '5832.bt1'], 'contains': ['23328.d1', '23328.h1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [41091120, 6227827207], 'label': '46656.ir.11664.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '11664.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715092
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.eo1', '3888.ep1', '3888.fn1', '5832.h1', '5832.p1', '5832.bd1', '5832.bz1', '5832.ca1', '5832.cb1', '5832.ci1'], 'contains': ['23328.e1', '23328.f1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1174320, 6267744000], 'label': '46656.ir.11664.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '11664.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715093
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bg1', '24.cg1'], 'contains': ['96.h1', '96.w1', '96.y1', '144.dr1', '144.ec1', '144.ed1', '144.ee1', '144.ef1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1174327, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.48.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216715094
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '729.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.er1', '3888.es1', '3888.et1', '3888.fo1', '3888.fp1', '5832.b1', '5832.q1', '5832.bu1', '5832.bz1', '5832.cc1', '5832.cd1', '5832.cj1'], 'contains': ['23328.e1', '23328.g1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [39957120, 1134007], 'label': '46656.ir.11664.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '11664.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715095
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.eq1', '3888.eu1', '3888.fq1', '5832.i1', '5832.n1', '5832.bv1', '5832.ca1', '5832.ce1', '5832.cf1', '5832.cj1'], 'contains': ['23328.e1', '23328.g1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39916807, 39957120], 'label': '46656.ir.11664.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '11664.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715096
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.ev1', '3888.ew1', '3888.fr1', '5832.j1', '5832.r1', '5832.z1', '5832.bz1', '5832.ce1', '5832.cg1', '5832.ck1'], 'contains': ['23328.e1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [1174320, 6227827207], 'label': '46656.ir.11664.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '11664.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715097
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.ex1', '3888.ey1', '3888.ez1', '3888.fs1', '5832.i1', '5832.q1', '5832.bo1', '5832.bw1', '5832.cb1', '5832.cg1', '5832.ch1'], 'contains': ['23328.e1', '23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [41050807, 39957120], 'label': '46656.ir.11664.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '11664.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715098
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.fa1', '3888.fb1', '3888.fc1', '3888.ft1', '5832.j1', '5832.s1', '5832.bd1', '5832.bu1', '5832.cf1', '5832.ch1', '5832.cl1'], 'contains': ['23328.e1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267744007, 1174320], 'label': '46656.ir.11664.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '11664.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715099
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kj1', '3888.fd1', '3888.fh1', '3888.fl1', '5832.k1', '5832.o1', '5832.bf1', '5832.cc1', '5832.ce1', '5832.ch1', '5832.ci1'], 'contains': ['23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6227464320, 1174320], 'label': '46656.ir.11664.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '11664.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715100
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kk1', '3888.fe1', '3888.fi1', '5832.k1', '5832.p1', '5832.bi1', '5832.bx1', '5832.cd1', '5832.cf1', '5832.cg1'], 'contains': ['23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [6267381120, 1174320], 'label': '46656.ir.11664.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '11664.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715101
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.kl1', '3888.ff1', '3888.fj1', '5832.l1', '5832.r1', '5832.bf1', '5832.bv1', '5832.cb1', '5832.cd1', '5832.cl1'], 'contains': ['23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [1174320, 6227464327], 'label': '46656.ir.11664.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '11664.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715102
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.km1', '3888.fg1', '3888.fk1', '3888.fm1', '5832.l1', '5832.s1', '5832.bi1', '5832.bw1', '5832.ca1', '5832.cc1', '5832.ck1'], 'contains': ['23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [6267381127, 1174320], 'label': '46656.ir.11664.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '11664.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715103
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.fu1', '3888.fv1', '3888.fw1', '3888.fx1', '5832.t1', '5832.bo1', '5832.bx1', '5832.ci1', '5832.cj1', '5832.ck1', '5832.cl1'], 'contains': ['23328.e1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800], 'label': '46656.ir.11664.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '11664.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 216715104
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '3.a1'], 'contains': ['12.c1', '12.bm1', '12.bn1', '12.br1', '12.bs1', '12.bx1', '12.by1', '18.x1', '54.be1', '54.bm1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 7, 41051125, 6227827818, 269279866800, 1521641624], 'label': '46656.ir.6.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715105
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1', '24.k1', '24.bb1', '24.ch1'], 'contains': ['96.c1', '96.h1', '96.bg1', '144.ds1', '144.eh1', '144.ei1', '144.ej1', '144.ek1', '144.el1', '144.em1', '144.en1'], 'core': '96.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827200, 41091127], 'label': '46656.ir.48.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216715106
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.fy1', '3888.fz1', '3888.gg1', '3888.gh1', '5832.a1', '5832.bt1', '5832.bz1'], 'contains': ['23328.f1', '23328.g1', '23328.h1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [39916807, 6227827207], 'label': '46656.ir.11664.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '11664.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715107
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.ga1', '3888.gb1', '3888.gc1', '3888.gi1', '3888.gj1', '3888.gk1', '3888.gl1', '5832.g1', '5832.u1', '5832.bz1'], 'contains': ['23328.f1', '23328.h1', '23328.j1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [6227827207, 41091127], 'label': '46656.ir.11664.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '11664.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715108
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.gd1', '3888.ge1', '3888.gf1', '3888.gm1', '3888.gn1', '5832.g1', '5832.bd1', '5832.bt1'], 'contains': ['23328.f1', '23328.i1', '23328.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [6267744007, 1174327], 'label': '46656.ir.11664.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.a1', 'old_label': '11664.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715109
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.lu1', '1296.lw1', '1296.ly1', '3888.go1', '5832.m1', '5832.bm1', '5832.by1'], 'contains': ['23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [1174789, 6227752218], 'label': '46656.ir.11664.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.k1', 'old_label': '11664.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715110
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '11664.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.lv1', '1296.lx1', '1296.lz1', '3888.gp1', '5832.m1', '5832.bn1', '5832.by1'], 'contains': ['23328.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': None, 'generators': [6267669018, 1174789], 'label': '46656.ir.11664.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1458.c1', 'old_label': '11664.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11664.bn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715111
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['5184.a1', '5184.b1', '5184.c1', '5184.d1', '5184.e1', '5184.f1', '5184.g1', '5184.h1', '5184.i1', '7776.a1', '7776.k1', '7776.l1', '7776.u1', '7776.ba1', '7776.bf1', '7776.bo1', '7776.bu1', '7776.ca1', '7776.cg1', '7776.co1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [435], 'label': '46656.ir.15552.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5184.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '15552.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715112
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.b1', '5184.j1', '5184.k1', '5184.l1', '5184.m1', '7776.b1', '7776.f1', '7776.g1', '7776.m1', '7776.x1', '7776.bb1', '7776.bd1', '7776.bi1', '7776.bm1', '7776.bp1', '7776.br1', '7776.bz1', '7776.cb1', '7776.ch1', '7776.cp1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37885034880], 'label': '46656.ir.15552.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '15552.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715113
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.c1', '5184.j1', '5184.n1', '5184.o1', '5184.p1', '5184.q1', '5184.r1', '5184.s1', '5184.t1', '7776.h1', '7776.n1', '7776.y1', '7776.bj1', '7776.bs1', '7776.ci1', '7776.cq1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [301891126320], 'label': '46656.ir.15552.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '15552.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715114
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.d1', '5184.j1', '5184.m1', '5184.n1', '5184.u1', '5184.v1', '5184.w1', '7776.c1', '7776.i1', '7776.o1', '7776.s1', '7776.z1', '7776.be1', '7776.bg1', '7776.bk1', '7776.bn1', '7776.bt1', '7776.bv1', '7776.cc1', '7776.cj1', '7776.cn1', '7776.cr1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080], 'label': '46656.ir.15552.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '15552.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715115
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['5184.b1', '5184.e1', '5184.k1', '5184.o1', '5184.u1', '5184.v1', '5184.x1', '5184.x2', '5184.y1', '5184.y2', '7776.d1', '7776.p1', '7776.bc1', '7776.bq1', '7776.cd1', '7776.ck1', '7776.cs1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1481684835], 'label': '46656.ir.15552.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '15552.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715116
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '24.s1', '24.bg1', '24.ch1', '24.ci1', '24.cj1', '24.ck1'], 'contains': ['96.h1', '96.o1', '144.eo1', '144.ep1', '144.eq1', '144.er1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827200, 1174645], 'label': '46656.ir.48.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1', 'subgroup_fusion': None, 'weyl_group': '576.8389'}
  • id: 216715117
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['5184.c1', '5184.f1', '5184.l1', '5184.o1', '5184.u1', '5184.w1', '5184.x1', '5184.x2', '5184.z1', '5184.ba1', '5184.bb1', '7776.q1', '7776.cl1', '7776.ct1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [294706903784], 'label': '46656.ir.15552.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '15552.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715118
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['5184.d1', '5184.g1', '5184.k1', '5184.l1', '5184.o1', '5184.p1', '5184.v1', '5184.w1', '5184.x1', '5184.x2', '5184.y1', '5184.y2', '5184.z1', '7776.e1', '7776.r1', '7776.bh1', '7776.bw1', '7776.ce1', '7776.cm1', '7776.cu1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624], 'label': '46656.ir.15552.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '15552.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715119
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.dw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3888.fv1', '5184.h1', '5184.q1', '5184.ba1', '7776.j1', '7776.t1', '7776.v1', '7776.bl1', '7776.bx1', '7776.cf1', '7776.cv1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [655477406640], 'label': '46656.ir.15552.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '15552.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715120
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '15552.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.bb1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3888.fw1', '5184.h1', '5184.i1', '5184.r1', '5184.ba1', '5184.bb1', '7776.w1', '7776.by1', '7776.cw1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [195089010864], 'label': '46656.ir.15552.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ex1', 'old_label': '15552.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15552.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 216715121
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.a1', '7776.b1', '7776.c1', '7776.d1', '7776.e1', '7776.f1', '11664.a1', '11664.b1', '11664.c1', '11664.d1', '11664.e1', '11664.f1', '11664.g1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916800], 'label': '46656.ir.23328.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '23328.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715122
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.g1', '7776.h1', '7776.i1', '7776.j1', '7776.k1', '11664.a1', '11664.h1', '11664.i1', '11664.j1', '11664.k1', '11664.l1', '11664.m1', '11664.n1', '11664.o1', '11664.p1', '11664.q1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7], 'label': '46656.ir.23328.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2592.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '23328.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715123
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.l1', '7776.m1', '7776.n1', '7776.o1', '7776.p1', '7776.q1', '7776.r1', '7776.s1', '7776.t1', '11664.b1', '11664.h1', '11664.r1', '11664.s1', '11664.t1', '11664.u1', '11664.v1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6227827200], 'label': '46656.ir.23328.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '23328.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715124
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.u1', '7776.v1', '7776.w1', '7776.x1', '7776.y1', '7776.z1', '11664.c1', '11664.i1', '11664.r1', '11664.w1', '11664.x1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41091120], 'label': '46656.ir.23328.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '23328.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715125
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.ba1', '7776.bb1', '7776.bc1', '7776.bd1', '7776.be1', '11664.c1', '11664.g1', '11664.j1', '11664.v1', '11664.y1', '11664.z1', '11664.ba1', '11664.bb1', '11664.bc1', '11664.bd1', '11664.be1', '11664.bf1', '11664.bg1', '11664.bh1', '11664.bi1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120], 'label': '46656.ir.23328.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '23328.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715126
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.bf1', '7776.bg1', '7776.bh1', '7776.bi1', '7776.bj1', '7776.bk1', '7776.bl1', '11664.b1', '11664.k1', '11664.r1', '11664.y1', '11664.bj1', '11664.bk1', '11664.bl1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744000], 'label': '46656.ir.23328.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '23328.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715127
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1', '24.bh1'], 'contains': ['96.k1', '96.l1', '96.q1', '144.dt1', '144.dw1', '144.es1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091120, 325, 270715782960, 40323593520, 6227827200, 461482882830], 'label': '46656.ir.48.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216715128
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.bm1', '7776.bn1', '7776.bo1', '7776.bp1', '7776.bq1', '11664.a1', '11664.d1', '11664.s1', '11664.w1', '11664.z1', '11664.ba1', '11664.bj1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39916807], 'label': '46656.ir.23328.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '23328.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715129
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.br1', '7776.bs1', '7776.bt1', '7776.bu1', '7776.bv1', '7776.bw1', '7776.bx1', '7776.by1', '11664.e1', '11664.h1', '11664.t1', '11664.x1', '11664.bb1', '11664.bj1', '11664.bk1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [6227827207], 'label': '46656.ir.23328.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.m1', 'old_label': '23328.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715130
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.bz1', '7776.ca1', '7776.cb1', '7776.cc1', '7776.cd1', '7776.ce1', '11664.d1', '11664.f1', '11664.j1', '11664.t1', '11664.w1', '11664.bc1', '11664.bl1', '11664.bm1', '11664.bn1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [39957127], 'label': '46656.ir.23328.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '23328.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715131
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.cf1', '7776.cg1', '7776.ch1', '7776.ci1', '7776.cj1', '7776.ck1', '7776.cl1', '7776.cm1', '11664.f1', '11664.i1', '11664.u1', '11664.z1', '11664.bk1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 243, 'diagramx': None, 'generators': [41091127], 'label': '46656.ir.23328.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '23328.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715132
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '23328.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7776.cn1', '7776.co1', '7776.cp1', '7776.cq1', '7776.cr1', '7776.cs1', '7776.ct1', '7776.cu1', '7776.cv1', '7776.cw1', '11664.e1', '11664.k1', '11664.s1', '11664.u1', '11664.x1', '11664.bd1', '11664.bl1'], 'contains': ['46656.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 486, 'diagramx': None, 'generators': [6267744007], 'label': '46656.ir.23328.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '23328.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '23328.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715133
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '46656.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['15552.a1', '15552.b1', '15552.c1', '15552.d1', '15552.e1', '15552.f1', '15552.g1', '15552.h1', '15552.i1', '23328.a1', '23328.b1', '23328.c1', '23328.d1', '23328.e1', '23328.f1', '23328.g1', '23328.h1', '23328.i1', '23328.j1', '23328.k1'], 'contains': [], 'core': '46656.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '46656.ir.46656.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '46656.a1', 'normal_contained_in': ['1728.a1', '5184.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '46656.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '46656.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 216715134
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.x1', '16.i1', '24.z1'], 'contains': ['96.i1', '96.m1', '96.s1', '144.dx1', '144.es1', '144.et1'], 'core': '864.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [41091120, 39366316080, 622713415418, 325, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.48.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '48.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1', 'subgroup_fusion': None, 'weyl_group': '648.299'}
  • id: 216715135
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.cb1', '16.j1', '24.z1'], 'contains': ['96.i1', '96.z1', '96.bc1', '144.ej1', '144.eu1', '144.ev1', '144.ew1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 622713415418, 325, 1481684400, 269279866800, 6227827200, 41091127], 'label': '46656.ir.48.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '48.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216715136
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.j1'], 'contains': ['96.j1', '96.ba1', '96.be1', '144.ek1', '144.eu1', '144.ew1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [40323593624, 195088320270, 270715782960, 40323593520, 6227827200, 34096648645, 41091127], 'label': '46656.ir.48.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bn1', 'old_label': '48.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1', 'subgroup_fusion': None, 'weyl_group': '972.460'}
  • id: 216715137
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1', '24.bh1'], 'contains': ['96.k1', '96.bb1', '96.bh1', '144.eg1', '144.en1', '144.eu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 325, 270715782960, 40323593520, 6227827200, 461482882830, 41091127], 'label': '46656.ir.48.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715138
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1', '24.bh1'], 'contains': ['96.l1', '96.x1', '96.bh1', '144.ex1', '144.fc1', '144.fd1', '144.fg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091120, 325, 270715782960, 40323593520, 6227827207, 461482882830], 'label': '46656.ir.48.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715139
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '24.m1', '24.cg1', '24.cm1'], 'contains': ['96.b1', '96.t1', '96.y1', '144.ey1', '144.ez1', '144.fa1', '144.fh1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 269279866800, 39957127], 'label': '46656.ir.48.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715140
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.y1', '16.k1', '24.z1'], 'contains': ['96.m1', '96.u1', '96.bc1', '144.fc1', '144.fi1', '144.fj1', '144.fk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [41091120, 39366316080, 622713415418, 325, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.48.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '48.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216715141
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['5832.v1', '5832.bp1', '5832.bq1', '5832.w1', '5832.x1', '5832.bs1', '5832.br1', '5832.y1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '24.a1', '24.x1', '24.y1', '32.c1', '216.cg1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.8.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '24.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216715142
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.z1', '16.k1'], 'contains': ['96.n1', '96.v1', '96.bd1', '144.fd1', '144.fi1', '144.fk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 1481684504, 269279866800, 455107081395, 6227827207], 'label': '46656.ir.48.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bs1', 'old_label': '48.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1', 'subgroup_fusion': None, 'weyl_group': '972.459'}
  • id: 216715143
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1', '24.n1', '24.bb1', '24.cg1'], 'contains': ['96.b1', '96.w1', '96.bg1', '144.fb1', '144.fe1', '144.ff1', '144.fg1', '144.fi1'], 'core': '96.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.48.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216715144
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '24.t1', '24.bo1', '24.cn1', '24.co1', '24.cp1', '24.cw1'], 'contains': ['96.o1', '96.p1', '144.fl1', '144.fs1', '144.ft1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 269279866800, 1174645, 6267744000], 'label': '46656.ir.48.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216715145
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.f1', '24.u1', '24.ch1', '24.cn1', '24.cq1', '24.cr1'], 'contains': ['96.c1', '96.o1', '96.t1', '144.fm1', '144.fn1', '144.fu1', '144.fv1', '144.fw1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 1134007, 325, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.48.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715146
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '24.m1', '24.r1', '24.ci1', '24.co1', '24.cs1', '24.ct1'], 'contains': ['96.o1', '96.t1', '144.fo1', '144.fx1', '144.fy1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 325, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.48.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715147
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '24.v1', '24.bg1', '24.cn1', '24.cs1', '24.cu1', '24.db1'], 'contains': ['96.o1', '96.w1', '144.fp1', '144.fz1', '144.ga1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827207, 1174645], 'label': '46656.ir.48.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715148
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.m1', '24.u1', '24.cj1', '24.cp1', '24.cu1', '24.cv1'], 'contains': ['96.o1', '96.y1', '144.fq1', '144.gb1', '144.gc1', '144.gd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 325, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.48.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715149
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '24.w1', '24.bo1', '24.ch1', '24.ct1', '24.cv1', '24.de1'], 'contains': ['96.o1', '96.bg1', '144.fr1', '144.ge1', '144.gf1', '144.gg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.48.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715150
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '24.s1', '24.bq1', '24.cq1', '24.cs1', '24.cv1', '24.cw1'], 'contains': ['96.o1', '144.gh1', '144.gj1', '144.gn1', '432.ja1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6227464320, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.48.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1', 'subgroup_fusion': None, 'weyl_group': '576.8389'}
  • id: 216715151
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '24.t1', '24.bt1', '24.ck1', '24.cr1', '24.ct1', '24.cu1'], 'contains': ['96.o1', '144.gk1', '144.go1', '432.jb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.48.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216715152
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.d1', '4.e1', '4.f1', '4.g1', '4.h1', '4.i1'], 'contains': ['16.a1', '24.c1', '24.ba1', '32.a1', '216.hm1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.8.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.d1', '4.e1', '4.f1', '4.g1', '4.h1', '4.i1'], 'normal_contains': ['16.a1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715153
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.v1', '24.bq1', '24.ci1', '24.cp1', '24.cr1', '24.de1'], 'contains': ['96.o1', '144.gl1', '144.gp1', '432.jc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227464327, 1481684504, 269279866800, 1174645], 'label': '46656.ir.48.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715154
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '24.w1', '24.bt1', '24.cj1', '24.co1', '24.cq1', '24.db1'], 'contains': ['96.o1', '144.gi1', '144.gm1', '144.gq1', '432.jd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 269279866800, 1174645], 'label': '46656.ir.48.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715155
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.x1', '24.ba1', '24.cl1', '24.cx1', '24.cy1', '24.cz1', '24.dc1'], 'contains': ['144.a1', '144.gs1', '144.gt1', '192.b1', '1296.jz1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 622713012218, 41051125, 269279866800], 'label': '46656.ir.48.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216715156
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '24.y1', '24.da1', '24.dd1'], 'contains': ['144.gs1', '144.gt1', '192.c1', '1296.ka1'], 'core': '432.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [39366316080, 461333739315, 39957120, 41050800, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.48.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '48.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715157
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '24.cg1', '24.cn1'], 'contains': ['96.p1', '96.t1', '96.w1', '144.gu1', '144.gv1', '144.hb1', '144.hc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.48.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216715158
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1', '24.k1', '24.bb1', '24.cn1'], 'contains': ['96.c1', '96.p1', '96.w1', '144.gw1', '144.gx1', '144.gy1', '144.hd1', '144.he1', '144.hf1'], 'core': '96.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207, 41091127], 'label': '46656.ir.48.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216715159
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1', '24.bh1'], 'contains': ['96.q1', '96.x1', '96.bb1', '144.gy1', '144.hg1', '144.hh1', '144.hi1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 325, 270715782960, 40323593520, 6227827207, 461482882830, 41091127], 'label': '46656.ir.48.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '48.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715160
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '24.bo1', '24.cg1'], 'contains': ['96.p1', '96.y1', '96.bg1', '144.gz1', '144.ha1', '144.hj1', '144.hk1', '144.hl1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6267744007, 1174327, 39366316080, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.48.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216715161
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.cd1', '16.l1', '24.z1'], 'contains': ['96.s1', '96.u1', '96.z1', '144.he1', '144.hg1', '144.hm1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [624190336641, 39366316080, 1481684400, 1481684504, 269279866800, 6227827207, 41091127], 'label': '46656.ir.48.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '48.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216715162
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '24.bx1', '24.cm1'], 'contains': ['96.y1', '144.hn1', '432.mg1', '432.mi1', '432.mk1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1174327, 39366316080, 325, 1481684400, 1481684504, 269279866800, 6227752218], 'label': '46656.ir.48.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1', 'subgroup_fusion': None, 'weyl_group': '2592.ot'}
  • id: 216715163
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['23328.c1', '23328.f1', '23328.k1', '23328.h1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.h1', '4.i1', '6.l1', '8.l1', '18.o1', '54.n1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 7, 41051125, 6227827818, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.2.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.h1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '46656.ir', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715164
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['5832.bc1', '5832.by1', '5832.m1', '5832.e1', '5832.ba1', '5832.c1', '5832.f1', '5832.bb1', '5832.d1', '5832.bq1', '5832.br1', '5832.bp1', '5832.bs1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.d1', '4.j1'], 'contains': ['16.a1', '24.ck1', '24.cl1', '32.b1', '216.is1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 6227827200, 461482882830, 1521641624], 'label': '46656.ir.8.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.d1', '4.j1'], 'normal_contains': ['16.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216715165
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '24.by1', '24.cm1'], 'contains': ['96.y1', '144.ho1', '432.mh1', '432.mj1', '432.ml1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1174327, 39366316080, 6267669018, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.48.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '48.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1', 'subgroup_fusion': None, 'weyl_group': '7776.lb'}
  • id: 216715166
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.e1'], 'contains': ['108.c1', '108.d1', '108.e1', '108.f1', '108.g1', '108.j1', '108.k1', '108.dv1', '108.dw1', '108.ed1', '108.ee1', '108.ef1', '108.eg1', '108.eu1', '108.ev1', '162.e1', '486.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 39916800, 1174645, 1174320, 6227827207, 499, 7, 104], 'label': '46656.ir.54.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '54.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715167
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '27.b1'], 'contains': ['108.n1', '108.p1', '108.r1', '108.dx1', '108.dy1', '108.em1', '108.eo1', '162.i1', '486.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 268280812800, 6227827207, 499, 7, 40320], 'label': '46656.ir.54.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216715168
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '27.b1'], 'contains': ['108.n1', '108.q1', '108.s1', '108.dz1', '108.ea1', '108.ep1', '108.eq1', '162.j1', '486.c1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 268280812800, 6227827207, 7, 39957619, 40320], 'label': '46656.ir.54.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715169
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '27.b1'], 'contains': ['108.o1', '108.p1', '108.s1', '108.ei1', '108.ej1', '108.en1', '108.er1', '162.k1', '486.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 6267381127, 268280812800, 499, 7, 40320], 'label': '46656.ir.54.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715170
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '27.b1'], 'contains': ['108.o1', '108.q1', '108.r1', '108.ek1', '108.el1', '108.es1', '108.et1', '162.l1', '486.e1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 6267381127, 268280812800, 7, 39957619, 40320], 'label': '46656.ir.54.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715171
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '27.c1'], 'contains': ['108.v1', '108.w1', '108.x1', '108.y1', '108.bb1', '108.cr1', '108.cs1', '108.ct1', '108.cu1', '108.cz1', '108.da1', '162.a1', '162.m1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 499, 1481684400, 443130957804, 269279866800, 40320, 1481684844], 'label': '46656.ir.54.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715172
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '27.c1'], 'contains': ['108.x1', '108.ba1', '108.bc1', '108.cv1', '108.cw1', '108.db1', '108.dc1', '162.b1', '486.g1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 443130957804, 269279866800, 40320, 39957619, 1481684844], 'label': '46656.ir.54.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715173
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '27.c1'], 'contains': ['108.y1', '108.z1', '108.bc1', '108.dd1', '108.de1', '108.df1', '108.di1', '162.c1', '486.k1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 499, 1481684400, 269279866800, 443609999724, 40320, 1481684844], 'label': '46656.ir.54.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715174
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '27.c1'], 'contains': ['108.z1', '108.ba1', '108.bb1', '108.dg1', '108.dh1', '108.dj1', '108.dk1', '162.d1', '486.l1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 269279866800, 443609999724, 40320, 39957619, 1481684844], 'label': '46656.ir.54.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715175
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['5832.bc1', '5832.e1', '5832.by1', '5832.m1', '5832.v1', '5832.x1', '5832.w1', '5832.y1', '5832.ba1', '5832.c1', '5832.bb1', '5832.f1', '5832.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.e1', '4.k1'], 'contains': ['16.a1', '24.cw1', '24.cx1', '32.d1', '216.jp1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 6267744000, 41050800, 1481684400, 39957120, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.8.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': ['4.b1', '4.e1', '4.k1'], 'normal_contains': ['16.a1', '72.c1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216715176
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '27.b1'], 'contains': ['108.be1', '108.bf1', '108.bg1', '108.bi1', '108.bl1', '108.ds1', '108.dt1', '108.dx1', '108.dz1', '108.ei1', '108.ek1', '162.e1', '486.f1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 39916800, 1174645, 1174320, 268280812800, 6227827207, 499, 7], 'label': '46656.ir.54.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715177
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '27.b1'], 'contains': ['108.bg1', '108.bk1', '108.bm1', '108.dy1', '108.ea1', '108.ej1', '108.el1', '162.f1', '486.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 39916800, 1174645, 1174320, 268280812800, 6227827207, 7, 39957619], 'label': '46656.ir.54.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715178
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '27.a1'], 'contains': ['108.bh1', '108.bo1', '108.bq1', '108.eh1', '108.ew1', '108.fh1', '108.fk1', '162.n1', '162.o1', '216.fx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 39916800, 6227827207, 7, 41051125, 174452060430], 'label': '46656.ir.54.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715179
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '27.a1'], 'contains': ['108.bh1', '108.ex1', '108.ey1', '162.p1', '216.gg1', '486.i1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39916800, 39957120, 499, 7, 41051125, 174452060430], 'label': '46656.ir.54.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715180
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '27.a1'], 'contains': ['108.bh1', '108.ez1', '108.fa1', '162.q1', '216.gh1', '486.j1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39916800, 39957120, 7, 41051125, 6227827818, 174452060430], 'label': '46656.ir.54.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715181
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '27.b1'], 'contains': ['108.bi1', '108.bj1', '108.bm1', '108.em1', '108.en1', '108.ep1', '108.es1', '162.g1', '486.k1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174320, 1174645, 39916800, 6267381127, 268280812800, 499, 7], 'label': '46656.ir.54.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715182
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '27.b1'], 'contains': ['108.bj1', '108.bk1', '108.bl1', '108.eo1', '108.eq1', '108.er1', '108.et1', '162.h1', '486.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174320, 1174645, 39916800, 6267381127, 268280812800, 7, 39957619], 'label': '46656.ir.54.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715183
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '27.b1'], 'contains': ['108.n1', '108.o1', '108.t1', '108.u1', '108.bg1', '108.bj1', '108.bn1', '108.br1', '108.bv1', '108.bw1', '108.bx1', '108.eb1', '108.fb1', '108.fg1', '108.fl1', '162.o1', '162.r1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39957120, 39916800, 268280812800, 6227827207, 7, 41051125], 'label': '46656.ir.54.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715184
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1', '27.b1'], 'contains': ['108.h1', '108.i1', '108.p1', '108.q1', '108.bi1', '108.bk1', '108.bt1', '108.bu1', '108.bv1', '108.fc1', '108.fd1', '162.p1', '486.o1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050800, 39957120, 39916800, 37885034880, 499, 7, 41051125, 31697930984], 'label': '46656.ir.54.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715185
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '27.b1'], 'contains': ['108.r1', '108.s1', '108.bl1', '108.bm1', '108.bv1', '108.fe1', '108.ff1', '162.q1', '486.p1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39916800, 39957120, 268280812800, 7, 6227827818, 41051125], 'label': '46656.ir.54.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715186
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['5832.v1', '5832.bp1', '5832.br1', '5832.y1', '5832.x1', '5832.bs1', '5832.bq1', '5832.w1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.j1', '4.k1'], 'contains': ['16.a1', '24.d1', '24.cy1', '32.f1', '216.jr1'], 'core': '8.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.8.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1', '4.j1', '4.k1'], 'normal_contains': ['16.a1', '24.d1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715187
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '27.c1'], 'contains': ['108.by1', '108.ca1', '108.cc1', '108.ct1', '108.cv1', '108.dd1', '108.dg1', '162.s1', '486.b1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 499, 1481684400, 443130957804, 39916800, 269279866800, 1481684844], 'label': '46656.ir.54.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715188
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '27.c1'], 'contains': ['108.by1', '108.cb1', '108.cd1', '108.cu1', '108.cw1', '108.df1', '108.dh1', '162.t1', '486.c1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 443130957804, 39916800, 269279866800, 39957619, 1481684844], 'label': '46656.ir.54.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715189
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '27.c1'], 'contains': ['108.bz1', '108.ca1', '108.cd1', '108.cz1', '108.db1', '108.de1', '108.dj1', '162.u1', '486.d1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 499, 1481684400, 39916800, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.54.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715190
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1', '27.c1'], 'contains': ['108.bz1', '108.cb1', '108.cc1', '108.da1', '108.dc1', '108.di1', '108.dk1', '162.v1', '486.e1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39916800, 269279866800, 443609999724, 39957619, 1481684844], 'label': '46656.ir.54.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.w1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715191
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.j1', '18.p1'], 'contains': ['108.a1', '108.b1', '108.l1', '108.m1', '108.ce1', '108.cf1', '108.cg1', '108.cj1', '108.cl1', '108.cm1', '108.cn1', '108.dq1', '108.dr1', '108.fi1', '108.fm1', '162.w1', '486.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 7, 1481684400, 39916800, 6227827207, 1521641624], 'label': '46656.ir.54.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '54.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.x1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715192
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1', '18.p1', '27.c1'], 'contains': ['108.x1', '108.z1', '108.bp1', '108.bs1', '108.by1', '108.bz1', '108.ci1', '108.ck1', '108.co1', '108.cp1', '108.cq1', '108.cx1', '108.dl1', '108.fj1', '108.fn1', '162.w1', '486.n1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 7, 269279866800], 'label': '46656.ir.54.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.y1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715193
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '18.n1', '27.c1'], 'contains': ['108.y1', '108.ba1', '108.ca1', '108.cb1', '108.co1', '108.dm1', '108.dn1', '162.x1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 499, 1521641964, 269279866800], 'label': '46656.ir.54.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.z1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715194
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1', '18.o1', '27.c1'], 'contains': ['108.bb1', '108.bc1', '108.cc1', '108.cd1', '108.co1', '108.do1', '108.dp1', '162.y1', '486.p1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 1481684400, 39957120, 39916800, 6227827818, 269279866800], 'label': '46656.ir.54.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.ba1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715195
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '18.q1', '27.c1'], 'contains': ['108.ct1', '108.cw1', '108.cx1', '108.de1', '108.dk1', '108.dm1', '108.do1', '162.z1', '486.q1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 499, 1481684400, 1521641964, 269279866800, 443609999724], 'label': '46656.ir.54.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715196
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '18.r1', '27.c1'], 'contains': ['108.cu1', '108.cv1', '108.cx1', '108.di1', '108.dj1', '108.dn1', '108.dp1', '162.ba1', '486.r1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39366316080, 39957120, 41050800, 1481684400, 1521641964, 269279866800, 443609999724], 'label': '46656.ir.54.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bc1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715197
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['5832.e1', '5832.by1', '5832.m1', '5832.bc1', '5832.ba1', '5832.c1', '5832.f1', '5832.bb1', '5832.d1', '5832.br1', '5832.bq1', '5832.bp1', '5832.bs1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.d1', '4.k1'], 'contains': ['16.a1', '24.cz1', '24.da1', '24.db1', '32.e1', '216.js1'], 'core': '8.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.8.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': ['4.c1', '4.d1', '4.k1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715198
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '18.s1', '27.c1'], 'contains': ['108.cz1', '108.dc1', '108.dd1', '108.dh1', '108.dl1', '108.dm1', '108.dp1', '162.bb1', '486.w1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1521641657, 6267744007, 39366316080, 39957120, 41050800, 7, 1481684400, 269279866800], 'label': '46656.ir.54.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bd1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715199
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '18.t1', '27.c1'], 'contains': ['108.da1', '108.db1', '108.df1', '108.dg1', '108.dl1', '108.dn1', '108.do1', '162.bc1', '486.x1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43633820302, 6267744007, 39366316080, 39957120, 41050800, 7, 1481684400, 269279866800], 'label': '46656.ir.54.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '54.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.be1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715200
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1', '27.b1'], 'contains': ['108.dx1', '108.ea1', '108.eb1', '108.en1', '108.et1', '108.fc1', '108.fe1', '162.bd1', '486.q1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39957120, 268280812800, 6227827207, 499, 7, 41051125], 'label': '46656.ir.54.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bf1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715201
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1', '27.b1'], 'contains': ['108.dy1', '108.dz1', '108.eb1', '108.er1', '108.es1', '108.fd1', '108.ff1', '162.be1', '486.r1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39957120, 268280812800, 6227827207, 7, 41051125, 39917299], 'label': '46656.ir.54.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bg1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715202
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '27.a1'], 'contains': ['108.eh1', '108.ex1', '108.ez1', '162.bd1', '216.gd1', '486.s1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 6227827207, 499, 7, 41051125, 174452060430], 'label': '46656.ir.54.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bh1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715203
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '27.a1'], 'contains': ['108.eh1', '108.ey1', '108.fa1', '162.be1', '216.ge1', '486.t1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 6227827207, 7, 41051125, 39917299, 174452060430], 'label': '46656.ir.54.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bi1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715204
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '27.a1'], 'contains': ['108.ew1', '108.ex1', '108.fa1', '162.bf1', '216.ic1', '486.u1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 6267744007, 41050800, 39957120, 499, 7, 41051125, 174452060430], 'label': '46656.ir.54.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bj1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715205
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '27.a1'], 'contains': ['108.ew1', '108.ey1', '108.ez1', '162.bg1', '216.id1', '486.v1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 6267744007, 41050800, 39957120, 7, 41051125, 6227827818, 174452060430], 'label': '46656.ir.54.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bk1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715206
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1', '27.b1'], 'contains': ['108.ei1', '108.el1', '108.em1', '108.eq1', '108.fb1', '108.fc1', '108.ff1', '162.bf1', '486.w1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 355459144424, 41050800, 39957120, 268280812800, 499, 7, 41051125], 'label': '46656.ir.54.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bl1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715207
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '54.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '27.b1'], 'contains': ['108.ej1', '108.ek1', '108.eo1', '108.ep1', '108.fb1', '108.fd1', '108.fe1', '162.bg1', '486.x1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 355459144424, 41050800, 39957120, 268280812800, 7, 41051125, 6227827818], 'label': '46656.ir.54.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bm1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715208
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['5832.bc1', '5832.e1', '5832.m1', '5832.by1', '5832.v1', '5832.x1', '5832.w1', '5832.y1', '5832.ba1', '5832.c1', '5832.bb1', '5832.f1', '5832.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.e1', '4.j1'], 'contains': ['16.a1', '24.dc1', '24.dd1', '24.de1', '32.g1', '216.jt1'], 'core': '8.g1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 41051125, 1481684400, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.8.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': ['4.c1', '4.e1', '4.j1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715209
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '32.a1', '32.b1', '32.c1', '32.d1', '32.e1', '32.f1', '32.g1'], 'contains': ['192.a1', '192.b1', '192.c1', '192.d1', '192.e1', '192.f1', '192.g1'], 'core': '192.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 461482882830], 'label': '46656.ir.64.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '64.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216715210
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['648.ha1', '648.hu1', '648.hv1', '648.hb1', '648.hd1', '648.hw1', '648.hx1', '648.hc1'], 'conjugacy_class_count': 1, 'contained_in': ['24.x1', '36.a1', '36.bq1', '36.bu1'], 'contains': ['144.a1', '216.a1', '288.bi1', '1944.by1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 623823424560], 'label': '46656.ir.72.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1', '36.a1'], 'normal_contains': ['144.a1', '216.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '46656.ir', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.9', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715211
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['648.o1', '648.bj1', '648.bl1', '648.ix1', '648.hh1', '648.hf1', '648.m1', '648.p1', '648.hg1', '648.n1', '648.hw1', '648.hv1', '648.hu1', '648.hx1'], 'conjugacy_class_count': 1, 'contained_in': ['24.cl1', '36.a1', '36.bx1', '36.dp1'], 'contains': ['144.a1', '216.jc1', '288.z1', '1944.fy1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827200, 623823424560], 'label': '46656.ir.72.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': ['8.c1', '36.a1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715212
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['648.ix1', '648.bj1', '648.bl1', '648.hh1', '648.o1', '648.ha1', '648.hc1', '648.hb1', '648.hd1', '648.hf1', '648.m1', '648.hg1', '648.p1', '648.n1'], 'conjugacy_class_count': 1, 'contained_in': ['24.cx1', '36.a1', '36.by1', '36.ds1'], 'contains': ['144.a1', '216.kw1', '288.cb1', '1944.gw1'], 'core': '72.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 623823424560, 6267744000], 'label': '46656.ir.72.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1', 'normal_contained_in': ['8.d1', '36.a1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '72.c1', 'projective_image': '46656.ir', 'quotient_action_image': '8.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715213
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.b1', '36.c1', '36.d1'], 'contains': ['144.b1', '144.c1', '144.f1', '144.bz1', '144.ck1', '144.ea1', '144.gu1', '216.b1', '216.d1', '216.e1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 39916800, 6227827207], 'label': '46656.ir.72.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715214
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '36.d1', '36.e1', '36.f1', '36.g1', '36.h1', '36.i1', '36.bn1'], 'contains': ['144.b1', '144.d1', '144.g1', '144.ce1', '144.ci1', '144.ey1', '144.fw1', '216.c1', '216.f1', '216.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 325, 1134000, 31697930984, 37885034880], 'label': '46656.ir.72.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715215
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.b1', '36.e1', '36.y1'], 'contains': ['144.b1', '144.cx1', '144.cy1', '216.h1', '216.l1', '648.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 499, 7, 325], 'label': '46656.ir.72.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '288.936'}
  • id: 216715216
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.g1', '36.y1', '36.z1'], 'contains': ['144.b1', '144.cz1', '144.dc1', '216.i1', '216.j1', '648.d1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1481684504, 1481684400, 7, 39957619, 325, 40320, 269279866800], 'label': '46656.ir.72.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715217
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.b1', '36.c1', '36.h1'], 'contains': ['144.b1', '144.da1', '144.de1', '216.m1', '216.n1', '648.e1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 7, 6227827818, 325], 'label': '46656.ir.72.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715218
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.c1', '36.e1', '36.z1'], 'contains': ['144.b1', '144.db1', '144.dd1', '216.k1', '216.o1', '648.f1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1134000, 268280812800, 31658054504, 37885034880, 7, 39957619, 325], 'label': '46656.ir.72.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715219
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.l1'], 'contains': ['16.b1', '16.c1', '16.d1', '16.i1', '16.j1', '16.k1', '16.l1', '24.z1', '24.bb1', '24.bh1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 6227827207, 7, 325, 269279866800, 461482882830], 'label': '46656.ir.8.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '8.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216715220
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.d1'], 'contains': ['144.c1', '144.f1', '144.g1', '144.ef1', '144.em1', '144.gx1', '144.ha1', '216.p1', '216.q1', '216.r1', '216.s1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1174327, 39366316080, 325, 1481684400, 1481684504, 39916800, 6227827207], 'label': '46656.ir.72.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715221
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '36.d1', '36.j1', '36.bo1'], 'contains': ['144.c1', '144.d1', '144.dv1', '144.er1', '144.fs1', '216.t1', '216.u1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 39916800, 6227827200, 1174645], 'label': '46656.ir.72.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715222
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.j1', '36.k1', '36.bn1'], 'contains': ['144.d1', '144.e1', '144.fa1', '144.fy1', '144.gd1', '216.v1', '216.x1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 325, 1134000, 31697930984, 37885034880], 'label': '46656.ir.72.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715223
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '36.d1', '36.k1', '36.bp1'], 'contains': ['144.d1', '144.f1', '144.ff1', '144.ga1', '144.gg1', '216.w1', '216.y1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 39916800, 6227827207, 1174645], 'label': '46656.ir.72.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715224
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1', '36.f1', '36.k1', '36.bo1'], 'contains': ['144.d1', '144.gn1', '144.go1', '216.z1', '648.bb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 39916800, 1174645], 'label': '46656.ir.72.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715225
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1', '36.f1', '36.j1', '36.bp1'], 'contains': ['144.d1', '144.gp1', '144.gq1', '216.ba1', '648.bc1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 39916800, 1174645], 'label': '46656.ir.72.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715226
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1', '36.i1'], 'contains': ['144.g1', '144.hn1', '144.ho1', '648.bj1', '648.bk1', '648.bl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1174327, 39366316080, 6267669018, 325, 1481684400, 1481684504, 39916800], 'label': '46656.ir.72.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '72.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
  • id: 216715227
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '36.l1'], 'contains': ['144.h1', '144.m1', '144.w1', '144.bp1', '144.bu1', '144.dz1', '144.hb1', '216.b1', '216.bh1', '216.bn1', '216.bo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 1481684504, 39916800, 269279866800, 6227827207], 'label': '46656.ir.72.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '72.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216715228
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.f1', '36.l1', '36.m1', '36.br1'], 'contains': ['144.h1', '144.q1', '144.bb1', '144.bs1', '144.bt1', '144.fh1', '144.fv1', '216.c1', '216.bi1', '216.bp1', '216.bq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 7, 1481684400, 269279866800, 1134000], 'label': '46656.ir.72.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715229
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.n1', '36.o1', '36.r1'], 'contains': ['144.i1', '144.k1', '144.x1', '144.bx1', '144.cj1', '144.dq1', '144.gv1', '216.d1', '216.bn1', '216.br1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 325, 39916800, 6227827207, 104], 'label': '46656.ir.72.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715230
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '4.l1'], 'contains': ['16.b1', '16.e1', '16.f1', '24.bc1', '24.bi1', '72.cl1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6227827207, 499, 7, 325, 269279866800, 461482882830], 'label': '46656.ir.8.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '8.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715231
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.p1', '36.q1', '36.r1'], 'contains': ['144.i1', '144.n1', '144.y1', '144.by1', '144.cm1', '144.eb1', '144.hc1', '216.e1', '216.bo1', '216.br1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 7, 325, 39916800, 40323593520, 6227827207], 'label': '46656.ir.72.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715232
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '36.r1', '36.s1', '36.t1'], 'contains': ['144.i1', '144.o1', '144.bc1', '144.cd1', '144.cg1', '144.ez1', '144.fm1', '216.g1', '216.bp1', '216.bs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 7, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.72.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715233
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1', '36.u1', '36.v1', '36.bn1'], 'contains': ['144.j1', '144.p1', '144.bd1', '144.ce1', '144.ch1', '144.fa1', '144.fn1', '216.f1', '216.bq1', '216.bs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.72.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715234
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.n1', '36.p1', '36.s1'], 'contains': ['144.i1', '144.cp1', '144.cq1', '216.l1', '216.bt1', '648.cf1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 268280812800, 499, 7, 325, 39916800, 104], 'label': '46656.ir.72.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715235
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.n1', '36.q1', '36.t1'], 'contains': ['144.i1', '144.cr1', '144.cv1', '216.m1', '216.bv1', '648.cg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 325, 39916800, 6227827818, 104], 'label': '46656.ir.72.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715236
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1', '36.o1', '36.p1', '36.t1'], 'contains': ['144.i1', '144.cs1', '144.cw1', '216.n1', '216.bv1', '648.ch1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 40323593520, 39916800, 268280812800, 7, 6227827818, 325], 'label': '46656.ir.72.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715237
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.o1', '36.q1', '36.s1'], 'contains': ['144.i1', '144.ct1', '144.cu1', '216.o1', '216.bw1', '648.ci1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 7, 325, 1481684400, 1481684504, 1134000, 39957619], 'label': '46656.ir.72.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715238
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1', '36.u1', '36.y1', '36.be1'], 'contains': ['144.j1', '144.cx1', '144.cz1', '216.h1', '216.bt1', '648.cj1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 499, 7, 325, 39916800, 31658054504, 37885034880], 'label': '46656.ir.72.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715239
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.v1', '36.y1', '36.bf1'], 'contains': ['144.j1', '144.cy1', '144.dc1', '216.i1', '216.bu1', '648.ck1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 7, 39957619, 325, 40320], 'label': '46656.ir.72.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715240
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1', '36.v1', '36.z1', '36.be1'], 'contains': ['144.j1', '144.cz1', '144.dd1', '216.j1', '216.bu1', '648.cl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 31658054504, 37885034880, 7, 39957619, 325, 40320], 'label': '46656.ir.72.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '72.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715241
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '4.l1'], 'contains': ['16.b1', '16.g1', '16.h1', '24.bf1', '24.bj1', '72.cm1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6227827207, 7, 41091619, 325, 269279866800, 461482882830], 'label': '46656.ir.8.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '8.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216715242
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1', '36.u1', '36.z1', '36.bf1'], 'contains': ['144.j1', '144.db1', '144.dc1', '216.k1', '216.bw1', '648.cm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 1134000, 39957619], 'label': '46656.ir.72.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715243
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.r1'], 'contains': ['144.k1', '144.y1', '144.bc1', '144.dr1', '144.ds1', '144.gw1', '144.gz1', '216.p1', '216.bx1', '216.by1', '216.bz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 1174327, 268280812800, 325, 39916800, 40323593520, 6227827207], 'label': '46656.ir.72.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715244
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.k1'], 'contains': ['144.l1', '144.v1', '144.z1', '144.ec1', '144.eh1', '144.hd1', '144.hj1', '216.r1', '216.by1', '216.cb1', '216.cc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684725, 1174327, 39366316080, 268280812800, 39916800, 6227827207, 104], 'label': '46656.ir.72.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '72.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216715245
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.k1', '36.l1'], 'contains': ['144.m1', '144.w1', '144.bb1', '144.ed1', '144.ej1', '144.he1', '144.hk1', '216.q1', '216.bx1', '216.cb1', '216.cc1', '216.cd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684835, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.72.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '72.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 216715246
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1', '36.r1'], 'contains': ['144.n1', '144.x1', '144.bc1', '144.ee1', '144.el1', '144.hf1', '144.hl1', '216.s1', '216.bz1', '216.cb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1174327, 39366316080, 268280812800, 325, 39916800, 6227827207, 104], 'label': '46656.ir.72.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715247
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1', '36.r1'], 'contains': ['144.k1', '144.n1', '144.o1', '144.dp1', '144.du1', '144.eo1', '144.fl1', '216.t1', '216.ca1', '216.ce1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 39916800, 6227827200, 104, 1174645], 'label': '46656.ir.72.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715248
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.l1', '36.l1', '36.w1', '36.bs1'], 'contains': ['144.m1', '144.q1', '144.dx1', '144.eq1', '144.ft1', '216.u1', '216.ce1', '216.cf1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 39916800, 269279866800, 6227827200], 'label': '46656.ir.72.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715249
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1', '36.bn1'], 'contains': ['144.p1', '144.t1', '144.u1', '144.ey1', '144.fa1', '144.fo1', '144.fq1', '216.v1', '216.ch1', '216.cl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.72.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715250
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1', '36.r1'], 'contains': ['144.o1', '144.x1', '144.y1', '144.fb1', '144.fe1', '144.fp1', '144.fr1', '216.w1', '216.ci1', '216.cm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 39916800, 6227827207, 104, 1174645], 'label': '46656.ir.72.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715251
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.m1', '36.w1', '36.x1', '36.br1'], 'contains': ['144.q1', '144.s1', '144.fh1', '144.fx1', '144.gc1', '216.x1', '216.cl1', '216.cn1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41050807, 39366316080, 1521641955, 39957120, 1481684400, 269279866800, 1134000], 'label': '46656.ir.72.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715252
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '4.l1'], 'contains': ['16.c1', '16.e1', '16.g1', '24.b1', '24.bk1', '72.cn1'], 'core': '24.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 499, 7, 325, 269279866800, 461482882830], 'label': '46656.ir.8.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '8.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216715253
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.n1', '36.l1', '36.x1', '36.bt1'], 'contains': ['144.q1', '144.w1', '144.fi1', '144.fz1', '144.gf1', '216.y1', '216.cm1', '216.co1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.72.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715254
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.o1', '36.m1', '36.x1', '36.bs1'], 'contains': ['144.q1', '144.gj1', '144.gk1', '216.z1', '216.cp1', '648.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267381120, 39366316080, 1481684835, 1174320, 1481684400, 39916800, 269279866800], 'label': '46656.ir.72.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715255
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.p1', '36.m1', '36.w1', '36.bt1'], 'contains': ['144.q1', '144.gl1', '144.gm1', '216.ba1', '216.cq1', '648.db1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 39916800, 6267381127, 269279866800], 'label': '46656.ir.72.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715256
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1', '36.y1', '36.z1', '36.bn1'], 'contains': ['144.b1', '144.e1', '144.j1', '144.t1', '144.be1', '144.ch1', '144.fo1', '216.bb1', '216.cu1', '216.cv1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 325, 1481684400, 39916800, 1521641624], 'label': '46656.ir.72.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715257
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1', '36.bn1'], 'contains': ['144.e1', '144.g1', '144.u1', '144.bd1', '144.be1', '144.fn1', '144.fq1', '216.be1', '216.cw1', '216.cx1', '216.cy1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 325, 1481684400, 39916800, 1521641624], 'label': '46656.ir.72.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715258
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '36.ba1', '36.bb1', '36.br1'], 'contains': ['144.h1', '144.s1', '144.bg1', '144.bt1', '144.fx1', '216.cu1', '216.da1', '216.db1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 39916800, 269279866800, 1521641624], 'label': '46656.ir.72.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715259
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1', '36.bc1', '36.bd1', '36.be1', '36.bf1', '36.bg1', '36.bh1', '36.bn1'], 'contains': ['144.j1', '144.u1', '144.bh1', '144.ci1', '144.fy1', '216.cv1', '216.db1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 325, 39916800, 31697930984, 37885034880], 'label': '46656.ir.72.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715260
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.s1', '36.bi1'], 'contains': ['144.bf1', '144.ep1', '144.gh1', '216.dc1', '216.dd1', '648.bp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 6227827200, 270715783064, 1481684400, 1174320, 1174645, 40320], 'label': '46656.ir.72.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '72.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715261
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.s1', '36.ba1', '36.bj1', '36.bs1'], 'contains': ['144.bg1', '144.eq1', '144.gj1', '216.dc1', '216.dd1', '216.de1', '648.bo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827200, 40320], 'label': '46656.ir.72.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 216715262
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1', '36.bc1', '36.bk1', '36.bo1'], 'contains': ['144.bh1', '144.er1', '144.gn1', '216.dc1', '648.bq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 6227827200, 40320, 1174645], 'label': '46656.ir.72.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715263
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '4.l1'], 'contains': ['16.c1', '16.f1', '16.h1', '24.bl1', '24.bn1', '72.co1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 7, 6227827818, 325, 269279866800, 461482882830], 'label': '46656.ir.8.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '8.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216715264
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1', '36.bd1', '36.bl1', '36.bo1'], 'contains': ['144.bh1', '144.fs1', '144.go1', '216.df1', '648.br1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 40320, 1174645], 'label': '46656.ir.72.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715265
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '36.bb1', '36.bm1', '36.bs1'], 'contains': ['144.bg1', '144.ft1', '144.gk1', '216.df1', '216.dg1', '648.bs1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 40320], 'label': '46656.ir.72.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715266
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '36.bi1'], 'contains': ['144.r1', '144.ba1', '144.bf1', '144.fu1', '144.gb1', '216.cw1', '216.dh1', '216.di1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 325, 39916800, 37885034880, 1521641624], 'label': '46656.ir.72.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '72.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715267
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '36.bj1', '36.bm1', '36.br1'], 'contains': ['144.s1', '144.bb1', '144.bg1', '144.fv1', '144.gc1', '216.cx1', '216.dh1', '216.di1', '216.dj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41050807, 39366316080, 1521641955, 39957120, 1481684400, 39916800, 269279866800], 'label': '46656.ir.72.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715268
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1', '36.bk1', '36.bl1', '36.bn1'], 'contains': ['144.t1', '144.bd1', '144.bh1', '144.fw1', '144.gd1', '216.cy1', '216.dh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 325, 39916800, 31697930984, 37885034880], 'label': '46656.ir.72.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715269
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '36.ba1', '36.bm1', '36.bt1'], 'contains': ['144.bg1', '144.fz1', '144.gl1', '216.dk1', '216.dl1', '648.bw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 269279866800, 40320, 6227827207], 'label': '46656.ir.72.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715270
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1', '36.bc1', '36.bl1', '36.bp1'], 'contains': ['144.bh1', '144.ga1', '144.gp1', '216.dl1', '648.bx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 40320], 'label': '46656.ir.72.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715271
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '36.bi1'], 'contains': ['144.bf1', '144.ge1', '144.gi1', '216.dm1', '216.dn1', '648.bz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 6267381127, 269278773445, 1174320, 1481684400, 355419187304, 40320], 'label': '46656.ir.72.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '72.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715272
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '36.bb1', '36.bj1', '36.bt1'], 'contains': ['144.bg1', '144.gf1', '144.gm1', '216.dm1', '216.dn1', '216.do1', '648.by1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 6267381127, 1481684835, 1174320, 1481684400, 269279866800, 40320], 'label': '46656.ir.72.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715273
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1', '36.bd1', '36.bk1', '36.bp1'], 'contains': ['144.bh1', '144.gg1', '144.gq1', '216.dm1', '648.ca1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 40320, 1174645], 'label': '46656.ir.72.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715274
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['23328.d1', '23328.j1', '23328.a1', '23328.g1', '23328.f1', '23328.k1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.f1', '4.h1', '6.m1', '8.i1', '18.q1', '54.bh1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 499, 7, 41051125, 269279866800, 1521641624, 461482882830], 'label': '46656.ir.2.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.f1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '46656.ir', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715275
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1', '4.l1'], 'contains': ['16.d1', '16.e1', '16.h1', '24.bz1', '24.cd1', '24.cf1', '72.cq1'], 'core': '48.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 455255499150, 7, 499, 325, 269279866800], 'label': '46656.ir.8.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '8.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216715276
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.bn1', '36.bo1', '36.bp1'], 'contains': ['144.d1', '144.p1', '144.be1', '144.bh1', '144.gr1', '216.cz1', '216.dp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 41051125, 39916800, 31697930984, 37885034880], 'label': '46656.ir.72.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715277
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '24.x1', '24.y1', '36.br1', '36.bs1', '36.bt1'], 'contains': ['144.q1', '144.bg1', '144.gs1', '216.a1', '216.dp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 41050800, 1481684400, 39916800, 269279866800], 'label': '46656.ir.72.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216715278
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.x1', '24.y1', '36.bv1'], 'contains': ['144.gt1', '216.a1', '288.bj1', '1944.bz1'], 'core': '216.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 463289990028], 'label': '46656.ir.72.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '72.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715279
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1', '24.z1', '36.bw1'], 'contains': ['144.bi1', '144.bj1', '144.bk1', '144.et1', '144.ev1', '144.fj1', '144.hm1', '216.dq1', '216.dw1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 39366316080, 624302466480, 7, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.72.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '72.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715280
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1', '18.q1', '36.bw1'], 'contains': ['144.bi1', '144.bl1', '144.bm1', '216.dr1', '216.dx1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 2917601004, 499, 24952072764, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '72.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216715281
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1', '18.r1', '36.bw1'], 'contains': ['144.bi1', '144.bn1', '144.bo1', '216.du1', '216.dy1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091619, 39366316080, 2917601004, 24952072764, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '72.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715282
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1', '18.n1', '36.bw1'], 'contains': ['144.bj1', '144.bl1', '144.bn1', '216.dz1', '216.eb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 39366316080, 2917601004, 499, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '72.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715283
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1', '18.o1', '36.bw1'], 'contains': ['144.bj1', '144.bm1', '144.bo1', '216.ea1', '216.ed1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 469, 39366316080, 624302466480, 1481684400, 6227827818, 269279866800], 'label': '46656.ir.72.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '72.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715284
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1', '36.bq1', '36.bx1', '36.by1', '36.bz1', '36.ca1', '36.cb1', '36.cc1'], 'contains': ['144.a1', '216.ep1', '288.g1', '1944.el1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 7, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715285
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1', '18.s1', '36.bw1'], 'contains': ['144.bk1', '144.bl1', '144.bo1', '216.eq1', '216.eu1', '216.ew1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684537, 7, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '72.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715286
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1', '4.l1'], 'contains': ['16.d1', '16.f1', '16.g1', '24.cb1', '24.ce1', '72.cr1'], 'core': '48.c1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 6227389338, 1481684400, 455255499150, 7, 325, 269279866800], 'label': '46656.ir.8.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '8.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': '11664.hy'}
  • id: 216715287
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1', '18.t1', '36.bw1'], 'contains': ['144.bk1', '144.bm1', '144.bn1', '216.es1', '216.ev1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6227388862, 6267744007, 39366316080, 7, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '72.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715288
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.z1', '24.bb1', '36.l1'], 'contains': ['144.bp1', '144.bs1', '144.bu1', '144.dx1', '144.ej1', '144.fi1', '144.he1', '216.dq1', '216.ex1', '216.ez1', '216.fa1', '216.fb1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.72.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '72.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 216715289
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bg1', '36.l1', '36.ba1', '36.cd1'], 'contains': ['144.bp1', '144.bt1', '144.ed1', '144.eq1', '144.fz1', '216.dv1', '216.fc1', '216.fd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 7, 1174320, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.72.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715290
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.z1', '24.bh1'], 'contains': ['144.bq1', '144.br1', '144.bv1', '144.es1', '144.eu1', '144.fc1', '144.hg1', '216.dw1', '216.ey1', '216.fb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 132379435521, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.72.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '72.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715291
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bo1', '36.l1', '36.bb1', '36.ce1'], 'contains': ['144.bt1', '144.bu1', '144.ft1', '144.gf1', '144.hk1', '216.ee1', '216.fe1', '216.ff1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.72.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715292
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bq1', '36.m1', '36.ba1', '36.ce1'], 'contains': ['144.bt1', '144.gj1', '144.gl1', '216.eg1', '216.fg1', '648.gu1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 7, 6227464327, 269279866800], 'label': '46656.ir.72.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715293
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bt1', '36.m1', '36.bb1', '36.cd1'], 'contains': ['144.bt1', '144.gk1', '144.gm1', '216.ej1', '216.fh1', '648.gv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 7, 269279866800], 'label': '46656.ir.72.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715294
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '24.ba1', '36.br1', '36.cd1', '36.ce1'], 'contains': ['144.bt1', '144.gc1', '144.gs1', '216.ep1', '216.fi1'], 'core': '432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 7, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.72.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cy1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216715295
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '36.r1', '36.cf1', '36.cg1'], 'contains': ['144.bx1', '144.cd1', '144.cm1', '144.dp1', '144.ds1', '144.fb1', '144.hf1', '216.ex1', '216.fj1', '216.fk1', '216.fl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 7, 325, 6227827207, 104], 'label': '46656.ir.72.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cz1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715296
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '36.n1', '36.cf1', '36.cn1'], 'contains': ['144.bx1', '144.cp1', '144.cr1', '216.fm1', '216.fq1', '216.fs1', '648.ds1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.72.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715297
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.b1', '18.c1', '18.d1', '18.f1', '18.g1', '18.h1', '18.i1', '18.j1', '18.k1', '18.l1', '18.u1', '18.v1', '18.w1', '18.x1', '81.a1', '81.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 499, 7, 41051125, 1521641624], 'label': '46656.ir.9.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715298
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1', '36.n1', '36.cg1', '36.co1'], 'contains': ['144.bx1', '144.cq1', '144.cv1', '216.fn1', '216.ft1', '648.dt1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39917299, 39366316080, 268280812800, 7, 325, 6227827207, 104], 'label': '46656.ir.72.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.db1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715299
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '36.o1', '36.cg1', '36.cn1'], 'contains': ['144.bx1', '144.cs1', '144.cu1', '216.fo1', '216.fu1', '648.du1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174819, 268280812800, 6227827207, 7, 104, 325], 'label': '46656.ir.72.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dc1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715300
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '36.o1', '36.cf1', '36.co1'], 'contains': ['144.bx1', '144.ct1', '144.cw1', '216.fp1', '216.fr1', '216.fv1', '648.dv1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 6227827207, 7, 104, 41091619, 325], 'label': '46656.ir.72.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dd1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715301
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1', '36.ch1'], 'contains': ['144.cb1', '144.cc1', '144.cn1', '144.dt1', '144.eg1', '144.ex1', '144.hi1', '216.ey1', '216.fk1', '216.fx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 300933848880, 7, 325, 382729979624, 457175461950, 6227827207], 'label': '46656.ir.72.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.de1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715302
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '36.r1', '36.ci1', '36.cj1'], 'contains': ['144.by1', '144.cd1', '144.cj1', '144.du1', '144.el1', '144.fe1', '144.gw1', '216.ez1', '216.fj1', '216.fy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091120, 268280812800, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.72.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715303
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '36.d1', '36.ck1', '36.cl1'], 'contains': ['144.bz1', '144.ce1', '144.ck1', '144.dv1', '144.em1', '144.ff1', '144.gx1', '216.fa1', '216.fl1', '216.fy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.72.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715304
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1', '24.bh1', '36.cm1'], 'contains': ['144.ca1', '144.cf1', '144.cl1', '144.dw1', '144.en1', '144.fg1', '144.gy1', '216.fb1', '216.fk1', '216.fy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 41091120, 7, 325, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.72.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '72.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dh1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715305
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '36.p1', '36.ci1', '36.cn1'], 'contains': ['144.by1', '144.cp1', '144.cs1', '216.fm1', '216.fz1', '648.ea1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 499, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.72.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.di1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715306
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1', '36.p1', '36.cj1', '36.co1'], 'contains': ['144.by1', '144.cq1', '144.cw1', '216.fn1', '216.ga1', '648.eb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 39917299, 268280812800, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.72.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dj1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715307
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '36.q1', '36.cj1', '36.cn1'], 'contains': ['144.by1', '144.cr1', '144.cu1', '216.fo1', '216.gb1', '648.ec1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 268280812800, 1174819, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.72.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dk1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715308
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['18.m1', '18.n1', '18.o1', '18.q1', '18.r1', '18.s1', '18.t1', '27.c1', '36.bw1', '243.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [623823424560, 39957120, 39916800, 39366316080, 499, 2957558124, 43673374524, 41050800, 269279866800, 1481684400], 'label': '46656.ir.9.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715309
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '36.q1', '36.ci1', '36.co1'], 'contains': ['144.by1', '144.ct1', '144.cv1', '216.fp1', '216.gc1', '648.ed1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091619, 268280812800, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.72.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715310
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '36.b1', '36.ck1', '36.cp1'], 'contains': ['144.bz1', '144.cx1', '144.da1', '216.fs1', '216.fz1', '648.ee1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6227827207, 499, 7, 325], 'label': '46656.ir.72.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dm1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715311
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1', '36.b1', '36.cl1', '36.cq1'], 'contains': ['144.bz1', '144.cy1', '144.de1', '216.ft1', '216.ga1', '648.ef1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39917299, 39366316080, 7, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.72.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715312
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.be1', '36.c1', '36.cl1', '36.cp1'], 'contains': ['144.bz1', '144.da1', '144.dd1', '216.fu1', '216.gb1', '648.eg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1174819, 1481684400, 6227827207, 7, 325], 'label': '46656.ir.72.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715313
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '36.c1', '36.ck1', '36.cq1'], 'contains': ['144.bz1', '144.db1', '144.de1', '216.fv1', '216.gc1', '648.eh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6227827207, 7, 41091619, 325], 'label': '46656.ir.72.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dp1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715314
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1', '24.bi1', '36.cm1'], 'contains': ['144.ca1', '144.df1', '144.dg1', '216.fq1', '216.fz1', '648.ei1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 40323593520, 6227827207, 499, 7, 325, 269279866800], 'label': '46656.ir.72.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '72.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dq1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715315
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1', '24.bj1', '36.cm1'], 'contains': ['144.ca1', '144.dh1', '144.di1', '216.fr1', '216.gc1', '648.ej1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 41091619, 7, 325, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.72.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '72.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dr1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715316
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1', '36.ch1'], 'contains': ['144.cb1', '144.dj1', '144.dk1', '216.fq1', '216.gd1', '648.ek1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [382729979624, 6227827207, 300933848880, 499, 7, 325, 461482882830], 'label': '46656.ir.72.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ds1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715317
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bj1', '36.ch1'], 'contains': ['144.cb1', '144.dl1', '144.dm1', '216.fr1', '216.ge1', '648.el1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091619, 300933848880, 7, 325, 382729979624, 457175461950, 6227827207], 'label': '46656.ir.72.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dt1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715318
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1', '36.r1', '36.cn1', '36.co1'], 'contains': ['144.bx1', '144.by1', '144.cg1', '144.dr1', '144.ee1', '144.eo1', '144.fp1', '216.fc1', '216.fw1', '216.gf1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 268280812800, 6227827207, 7, 104], 'label': '46656.ir.72.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715319
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.k1', '6.l1'], 'contains': ['24.a1', '24.c1', '24.d1', '24.f1', '24.m1', '24.r1', '24.u1', '36.bn1', '36.br1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.12.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '24.c1', '24.d1', '48.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715320
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1', '36.d1', '36.bc1', '36.cp1', '36.cq1', '36.cr1', '36.cs1', '36.ct1'], 'contains': ['144.bz1', '144.ci1', '144.ef1', '144.er1', '144.ga1', '216.fd1', '216.gf1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 7], 'label': '46656.ir.72.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715321
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '36.ch1'], 'contains': ['144.cc1', '144.dj1', '144.dl1', '216.gg1', '216.gm1', '648.eo1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [382729979624, 41091120, 457175461950, 300933848880, 499, 7, 325], 'label': '46656.ir.72.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dw1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715322
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '36.ch1'], 'contains': ['144.cc1', '144.dk1', '144.dm1', '216.gh1', '216.gn1', '648.ep1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 300933848880, 7, 325, 6227827818, 382729979624, 457175461950], 'label': '46656.ir.72.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dx1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715323
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.s1', '36.cf1', '36.ci1'], 'contains': ['144.cd1', '144.cp1', '144.ct1', '216.gi1', '216.gm1', '216.go1', '648.eq1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 499, 7, 325, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.72.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dy1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715324
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1', '36.s1', '36.cg1', '36.cj1'], 'contains': ['144.cd1', '144.cq1', '144.cu1', '216.gk1', '216.gp1', '648.er1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 301891126320, 7, 325, 1481684400, 1481684504, 39957619], 'label': '46656.ir.72.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dz1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715325
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '36.t1', '36.cf1', '36.cj1'], 'contains': ['144.cd1', '144.cr1', '144.cw1', '216.gl1', '216.gn1', '216.gq1', '648.es1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 7, 325, 6227827818, 104], 'label': '46656.ir.72.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ea1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715326
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '36.t1', '36.cg1', '36.ci1'], 'contains': ['144.cd1', '144.cs1', '144.cv1', '216.gl1', '216.gr1', '648.et1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091120, 268280812800, 7, 325, 6227827818, 40323593520], 'label': '46656.ir.72.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eb1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715327
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.e1', '36.u1', '36.ck1'], 'contains': ['144.ce1', '144.cx1', '144.db1', '216.gi1', '216.go1', '648.eu1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 268280812800, 499, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.72.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ec1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715328
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1', '36.e1', '36.v1', '36.cl1'], 'contains': ['144.ce1', '144.cy1', '144.dd1', '216.gj1', '216.gp1', '648.ev1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 325, 31658054504, 39957619, 37885034880], 'label': '46656.ir.72.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ed1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715329
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1', '36.g1', '36.u1', '36.v1'], 'contains': ['144.ce1', '144.cz1', '144.dc1', '216.gj1', '216.gk1', '648.ew1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 1481684400, 1481684504, 39957619], 'label': '46656.ir.72.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ee1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715330
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['3888.dw1', '3888.ef1', '3888.eg1', '3888.gl1', '3888.ea1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '6.a1', '6.m1', '6.o1'], 'contains': ['24.c1', '24.bp1', '24.bv1', '36.dj1', '108.dm1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 499, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.12.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': ['4.f1', '6.a1'], 'normal_contains': ['24.c1', '48.b1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '46656.ir', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715331
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1', '36.h1', '36.ck1', '36.cl1'], 'contains': ['144.ce1', '144.da1', '144.de1', '216.gq1', '216.gr1', '648.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 1481684400, 1481684504, 6227827818], 'label': '46656.ir.72.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ef1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715332
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.bk1', '36.cm1'], 'contains': ['144.cf1', '144.df1', '144.dh1', '216.gm1', '216.go1', '648.ey1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 7, 325, 269279866800, 104], 'label': '46656.ir.72.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '72.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eg1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715333
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '24.bn1', '36.cm1'], 'contains': ['144.cf1', '144.dg1', '144.di1', '216.gn1', '216.gr1', '648.ez1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 40323593520, 41091120, 7, 6227827818, 325, 269279866800], 'label': '46656.ir.72.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '72.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eh1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715334
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1', '36.r1', '36.cu1', '36.cv1'], 'contains': ['144.cg1', '144.cj1', '144.cm1', '144.fl1', '144.fr1', '144.gz1', '144.hl1', '216.fe1', '216.gs1', '216.hd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 1174320, 104, 1174645], 'label': '46656.ir.72.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ei1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715335
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1', '36.s1', '36.cn1', '36.cu1'], 'contains': ['144.cg1', '144.cp1', '144.cu1', '216.gt1', '216.hi1', '648.fb1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1481684400, 39957120, 499, 7, 301891126320, 325, 1521641624], 'label': '46656.ir.72.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ej1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715336
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1', '36.s1', '36.co1', '36.cv1'], 'contains': ['144.cg1', '144.cq1', '144.ct1', '216.gw1', '216.hj1', '648.fc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 7, 325, 1481684400, 1134499, 1521641624], 'label': '46656.ir.72.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ek1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715337
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1', '36.t1', '36.cn1', '36.cv1'], 'contains': ['144.cg1', '144.cr1', '144.cs1', '216.gy1', '216.hk1', '648.fd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 1174320, 6227827818, 104, 1174645], 'label': '46656.ir.72.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.el1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715338
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '36.t1', '36.co1', '36.cu1'], 'contains': ['144.cg1', '144.cv1', '144.cw1', '216.ha1', '216.hl1', '648.fe1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 6267744618, 268280812800, 7, 104], 'label': '46656.ir.72.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.em1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715339
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1', '36.u1', '36.y1', '36.dj1'], 'contains': ['144.ch1', '144.cx1', '144.dc1', '216.gt1', '216.he1', '648.ff1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 499, 7, 325, 1521641624], 'label': '46656.ir.72.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715340
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1', '36.u1', '36.z1', '36.dk1'], 'contains': ['144.ch1', '144.cz1', '144.db1', '216.gw1', '216.hf1', '648.fg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 325, 1481684400, 1134499, 1521641624], 'label': '46656.ir.72.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715341
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['3888.dw1', '3888.gl1', '3888.ef1', '3888.eg1', '3888.ea1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '6.a1', '6.n1', '6.p1'], 'contains': ['24.c1', '24.br1', '24.bs1', '36.dk1', '108.dn1'], 'core': '12.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 7, 41051125, 39917299, 269279866800, 1521641624], 'label': '46656.ir.12.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': ['4.g1', '6.a1'], 'normal_contains': ['24.c1', '48.c1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '46656.ir', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715342
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1', '36.v1', '36.y1', '36.dk1'], 'contains': ['144.ch1', '144.cy1', '144.cz1', '216.gv1', '216.hg1', '648.fh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39917299, 39366316080, 39957120, 7, 325, 1481684400, 1521641624], 'label': '46656.ir.72.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ep1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715343
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1', '36.v1', '36.z1', '36.dj1'], 'contains': ['144.ch1', '144.dc1', '144.dd1', '216.gz1', '216.hh1', '648.fi1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 7, 41051299, 325, 1521641624], 'label': '46656.ir.72.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '72.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715344
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1', '36.d1', '36.bd1', '36.cw1', '36.cx1', '36.cy1', '36.cz1', '36.di1'], 'contains': ['144.ci1', '144.ck1', '144.fs1', '144.gg1', '144.ha1', '216.ff1', '216.hd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.72.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.er1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715345
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bp1', '36.e1', '36.be1', '36.cp1', '36.cw1', '36.da1', '36.db1', '36.dj1'], 'contains': ['144.ci1', '144.cx1', '144.dd1', '216.he1', '216.hi1', '648.fk1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39957120, 268280812800, 37885034880, 499, 7, 325, 31697930984], 'label': '46656.ir.72.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.es1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715346
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bq1', '36.f1', '36.bc1', '36.da1', '36.dc1', '36.dd1', '36.de1', '36.di1'], 'contains': ['144.ci1', '144.gn1', '144.gp1', '216.fg1', '648.hk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6227464327], 'label': '46656.ir.72.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.et1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715347
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1', '36.e1', '36.bf1', '36.cq1', '36.cx1', '36.dc1', '36.df1', '36.dk1'], 'contains': ['144.ci1', '144.cy1', '144.db1', '216.hf1', '216.hj1', '648.fm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 325, 1134499, 31697930984, 37885034880], 'label': '46656.ir.72.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eu1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715348
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1', '36.g1', '36.be1', '36.cr1', '36.cy1', '36.dd1', '36.dg1', '36.dk1'], 'contains': ['144.ci1', '144.cz1', '216.hg1', '648.fn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39917299, 268280812800, 39957120, 7, 325, 31697930984, 37885034880], 'label': '46656.ir.72.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715349
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1', '36.f1', '36.bd1', '36.ct1', '36.db1', '36.df1', '36.dg1', '36.dh1'], 'contains': ['144.ci1', '144.go1', '144.gq1', '216.fh1', '648.hn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.72.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ew1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715350
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1', '36.h1', '36.bg1', '36.cp1', '36.cx1', '36.dd1', '36.dh1', '36.dl1'], 'contains': ['144.ci1', '144.da1', '216.hk1', '648.fp1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 1481684504, 6227827818, 1174645], 'label': '46656.ir.72.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ex1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715351
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1', '36.g1', '36.bf1', '36.cs1', '36.cz1', '36.de1', '36.dh1', '36.dj1'], 'contains': ['144.ci1', '144.dc1', '216.hh1', '648.fq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39957120, 268280812800, 37885034880, 7, 41051299, 325, 31697930984], 'label': '46656.ir.72.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715352
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.e1', '24.g1', '24.i1', '24.bc1', '24.bd1', '24.bz1', '24.ca1', '36.b1', '36.n1', '36.p1', '108.v1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 39916800, 6227827207, 499, 7, 325, 269279866800], 'label': '46656.ir.12.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216715353
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1', '36.h1', '36.bh1', '36.cq1', '36.cw1', '36.de1', '36.dg1', '36.dm1'], 'contains': ['144.ci1', '144.de1', '216.hl1', '648.fr1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267744618, 7], 'label': '46656.ir.72.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ez1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715354
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1', '36.i1', '36.bg1', '36.cr1', '36.cz1', '36.da1', '36.df1', '36.dm1'], 'contains': ['144.ci1', '144.hn1', '648.fs1', '648.hr1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6227464938, 7, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.72.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fa1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715355
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.by1', '36.i1', '36.bh1', '36.cs1', '36.cy1', '36.db1', '36.dc1', '36.dl1'], 'contains': ['144.ci1', '144.ho1', '648.ft1', '648.hs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 7, 1174320, 1481684400, 1481684504, 6267381738, 1174645], 'label': '46656.ir.72.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fb1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715356
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '36.bn1', '36.ct1', '36.di1', '36.dj1', '36.dk1', '36.dl1', '36.dm1'], 'contains': ['144.ch1', '144.ci1', '144.fq1', '144.gd1', '144.gr1', '216.fi1', '216.hn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050800, 39957120, 268280812800, 37885034880, 7, 41051125, 31697930984], 'label': '46656.ir.72.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fc1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715357
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '36.n1', '36.ci1', '36.cu1'], 'contains': ['144.cj1', '144.cp1', '144.cv1', '216.ho1', '216.hs1', '648.fv1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 499, 7, 325, 104], 'label': '46656.ir.72.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fd1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715358
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1', '36.n1', '36.cj1', '36.cv1'], 'contains': ['144.cj1', '144.cq1', '144.cr1', '216.hp1', '216.ht1', '648.fw1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 325, 6227827818, 104], 'label': '46656.ir.72.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fe1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715359
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1', '36.o1', '36.ci1', '36.cv1'], 'contains': ['144.cj1', '144.cs1', '144.ct1', '216.hq1', '216.hu1', '648.fx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 325, 6227389338, 104], 'label': '46656.ir.72.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ff1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715360
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1', '36.o1', '36.cj1', '36.cu1'], 'contains': ['144.cj1', '144.cu1', '144.cw1', '216.hr1', '216.hv1', '648.fy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 1174819, 7, 325, 104], 'label': '46656.ir.72.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fg1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715361
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '36.b1', '36.ck1', '36.cw1'], 'contains': ['144.ck1', '144.cx1', '144.de1', '216.ho1', '216.hy1', '648.fz1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 499, 7, 325], 'label': '46656.ir.72.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fh1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715362
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1', '36.b1', '36.cl1', '36.cx1'], 'contains': ['144.ck1', '144.cy1', '144.da1', '216.hp1', '216.hz1', '648.ga1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 1481684400, 1481684504, 6227827818], 'label': '46656.ir.72.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fi1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715363
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.e1', '24.i1', '24.j1', '24.be1', '24.bf1', '24.cb1', '24.cc1', '36.c1', '36.o1', '36.q1', '108.w1'], 'core': '48.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1174819, 1481684400, 39916800, 6227827207, 7, 325, 269279866800], 'label': '46656.ir.12.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216715364
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1', '36.c1', '36.ck1', '36.cx1'], 'contains': ['144.ck1', '144.da1', '144.db1', '216.hq1', '216.ia1', '648.gb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 6227389338, 1481684400, 7, 325], 'label': '46656.ir.72.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fj1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715365
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1', '36.c1', '36.cl1', '36.cw1'], 'contains': ['144.ck1', '144.dd1', '144.de1', '216.hr1', '216.ib1', '648.gc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1174819, 1481684400, 7, 325], 'label': '46656.ir.72.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fk1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715366
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '24.cd1', '24.cf1', '36.cm1'], 'contains': ['144.cl1', '144.df1', '144.di1', '216.ho1', '216.hw1', '648.gd1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 499, 7, 325, 269279866800, 104], 'label': '46656.ir.72.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '72.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fl1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715367
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1', '24.ce1', '36.cm1'], 'contains': ['144.cl1', '144.dg1', '144.dh1', '216.hq1', '216.hx1', '648.ge1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 6227389338, 269279866800, 104], 'label': '46656.ir.72.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '72.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fm1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715368
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1', '36.p1', '36.cf1', '36.cu1'], 'contains': ['144.cm1', '144.cp1', '144.cw1', '216.hs1', '216.hw1', '216.hy1', '648.gf1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 499, 7, 325, 40323593520], 'label': '46656.ir.72.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fn1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715369
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1', '36.p1', '36.cg1', '36.cv1'], 'contains': ['144.cm1', '144.cq1', '144.cs1', '216.ht1', '216.hz1', '648.gg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 7, 325, 6227827818, 40323593520], 'label': '46656.ir.72.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fo1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715370
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cb1', '36.q1', '36.cf1', '36.cv1'], 'contains': ['144.cm1', '144.cr1', '144.ct1', '216.hu1', '216.hx1', '216.ia1', '648.gh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 7, 325, 6227389338, 40323593520], 'label': '46656.ir.72.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fp1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715371
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1', '36.q1', '36.cg1', '36.cu1'], 'contains': ['144.cm1', '144.cu1', '144.cv1', '216.hv1', '216.ib1', '648.gi1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 1174819, 7, 325, 40323593520], 'label': '46656.ir.72.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fq1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715372
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1', '36.ch1'], 'contains': ['144.cn1', '144.dj1', '144.dm1', '216.hw1', '216.ic1', '648.gj1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267744007, 388956924720, 499, 7, 294706903784, 325, 174451657230], 'label': '46656.ir.72.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '72.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fr1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715373
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ce1', '36.ch1'], 'contains': ['144.cn1', '144.dk1', '144.dl1', '216.hx1', '216.id1', '648.gk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 6227389338, 388956924720, 7, 294706903784, 325, 174451657230], 'label': '46656.ir.72.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '72.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fs1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715374
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.c1', '6.k1'], 'contains': ['24.e1', '24.f1', '24.k1', '24.l1', '24.n1', '24.bb1', '24.bg1', '24.bo1', '24.cg1', '24.ch1', '24.cn1', '36.d1', '36.l1', '36.r1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6227827207, 7, 269279866800], 'label': '46656.ir.12.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715375
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cf1'], 'contains': ['144.co1', '144.dn1', '144.do1', '216.hw1', '648.gl1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6267744007, 388956924720, 499, 7, 455255499150, 294706903784, 325], 'label': '46656.ir.72.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '72.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ft1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216715376
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1', '36.r1'], 'contains': ['144.dp1', '144.dq1', '144.dr1', '144.ez1', '144.fe1', '144.hc1', '144.hl1', '216.ie1', '216.if1', '216.ig1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091120, 1174327, 268280812800, 325, 40323593520, 6227827207], 'label': '46656.ir.72.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fu1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715377
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1', '36.d1'], 'contains': ['144.dv1', '144.ea1', '144.ef1', '144.ey1', '144.ff1', '144.gu1', '144.ha1', '216.ie1', '216.il1', '216.im1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.72.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '72.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fv1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715378
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1', '36.r1'], 'contains': ['144.du1', '144.eb1', '144.ee1', '144.ez1', '144.fb1', '144.gv1', '144.gz1', '216.if1', '216.il1', '216.in1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 268280812800, 325, 6227827207, 104], 'label': '46656.ir.72.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fw1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715379
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cg1', '36.l1'], 'contains': ['144.dx1', '144.dz1', '144.ed1', '144.fh1', '144.fi1', '144.hb1', '144.hk1', '216.ig1', '216.im1', '216.in1', '216.io1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.72.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '72.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fx1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 216715380
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1', '36.r1'], 'contains': ['144.dq1', '144.ds1', '144.eb1', '144.el1', '144.eo1', '144.fm1', '144.fr1', '216.ii1', '216.ip1', '216.iq1', '216.ir1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 1174320, 6227827200, 104, 1174645], 'label': '46656.ir.72.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fy1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715381
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ch1', '36.bi1'], 'contains': ['144.dy1', '144.ei1', '144.ep1', '144.fu1', '144.ge1', '216.iq1', '216.it1', '216.iu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 39366316080, 269278773445, 1174320, 1481684400, 6227827200, 355419187304], 'label': '46656.ir.72.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '72.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fz1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715382
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ch1', '36.l1', '36.bj1', '36.do1'], 'contains': ['144.dz1', '144.ej1', '144.eq1', '144.fv1', '144.gf1', '216.ip1', '216.it1', '216.iu1', '216.iv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684835, 1174320, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.72.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ga1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715383
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1', '36.d1', '36.bk1', '36.dn1'], 'contains': ['144.ea1', '144.em1', '144.er1', '144.fw1', '144.gg1', '216.ir1', '216.it1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 1481684504, 6227827200, 1174645], 'label': '46656.ir.72.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gb1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715384
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ci1', '36.w1', '36.ba1', '36.do1'], 'contains': ['144.eq1', '144.fx1', '144.gl1', '216.iw1', '216.ix1', '648.ic1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40327, 39366316080, 1481684835, 1174320, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.72.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gc1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715385
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['23328.d1', '23328.j1', '23328.a1', '23328.g1', '23328.k1', '23328.f1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.g1', '4.i1', '6.n1', '8.j1', '18.r1', '54.bi1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 7, 41051125, 39917299, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.2.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.g1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '46656.ir', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715386
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.b1', '6.d1'], 'contains': ['24.b1', '24.f1', '24.g1', '24.j1', '24.bm1', '24.bp1', '24.br1', '36.e1', '36.s1', '36.u1', '108.y1'], 'core': '24.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 1134000, 499, 7, 325, 269279866800, 1521641624], 'label': '46656.ir.12.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715387
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1', '36.j1', '36.bc1', '36.dn1'], 'contains': ['144.er1', '144.fy1', '144.gp1', '216.ix1', '648.ig1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [40327, 39366316080, 1174320, 1481684400, 1481684504, 6227827200, 1174645], 'label': '46656.ir.72.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gd1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715388
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cj1', '36.bi1'], 'contains': ['144.ep1', '144.gb1', '144.gi1', '216.iy1', '216.iz1', '648.ii1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 6267381127, 269278773445, 1174320, 1481684400, 355419187304, 39957127], 'label': '46656.ir.72.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '72.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ge1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715389
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cj1', '36.w1', '36.bj1', '36.cd1'], 'contains': ['144.eq1', '144.gc1', '144.gm1', '216.iy1', '216.iz1', '216.ja1', '648.ih1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 6267381127, 1481684835, 1174320, 1481684400, 269279866800, 39957127], 'label': '46656.ir.72.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gf1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715390
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cj1', '36.j1', '36.bk1', '36.ct1'], 'contains': ['144.er1', '144.gd1', '144.gq1', '216.iy1', '648.ij1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 39957127, 1174645], 'label': '46656.ir.72.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gg1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715391
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ck1', '36.bo1', '36.ct1', '36.dn1'], 'contains': ['144.er1', '144.go1', '144.gr1', '216.jb1', '648.ik1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 6227827200, 1521641624], 'label': '46656.ir.72.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gh1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715392
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ck1', '24.cl1', '36.bs1', '36.cd1', '36.do1'], 'contains': ['144.eq1', '144.gk1', '144.gs1', '216.jb1', '216.jc1', '648.il1'], 'core': '432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 41050800, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.72.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gi1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715393
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cm1', '36.i1'], 'contains': ['144.ey1', '144.hn1', '144.ho1', '648.ix1', '648.iy1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 1174327, 39366316080, 6267669018, 325, 1481684400, 1481684504], 'label': '46656.ir.72.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '72.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gj1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
  • id: 216715394
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1', '36.r1'], 'contains': ['144.fl1', '144.fm1', '144.fp1', '144.gv1', '144.gw1', '144.hc1', '144.hf1', '216.jg1', '216.jo1', '216.jq1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 1174320, 6227827207, 104, 1174645], 'label': '46656.ir.72.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '72.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gk1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715395
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1', '36.d1', '36.bl1', '36.dq1'], 'contains': ['144.fs1', '144.fw1', '144.ga1', '144.gu1', '144.gx1', '216.jo1', '216.jy1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 1174320, 1481684400, 1481684504, 6227827207, 1174645], 'label': '46656.ir.72.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gl1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715396
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1', '36.j1', '36.bd1', '36.dq1'], 'contains': ['144.fs1', '144.fy1', '144.gq1', '216.jz1', '648.ja1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [40327, 39366316080, 6267381127, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.72.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gm1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715397
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.e1', '6.k1'], 'contains': ['24.f1', '24.o1', '24.p1', '24.bq1', '24.bt1', '24.cq1', '24.cr1', '36.f1', '36.m1', '108.bj1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6267381127, 7, 269279866800], 'label': '46656.ir.12.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715398
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cp1', '36.j1', '36.bl1', '36.di1'], 'contains': ['144.fs1', '144.gd1', '144.gp1', '216.ka1', '648.jb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39957127, 6227464327], 'label': '46656.ir.72.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gn1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715399
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cn1', '36.l1', '36.bm1', '36.dr1'], 'contains': ['144.ft1', '144.fv1', '144.fz1', '144.hb1', '144.he1', '216.jq1', '216.jy1', '216.kb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684835, 1174320, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.72.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.go1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715400
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.co1', '36.w1', '36.bb1', '36.dr1'], 'contains': ['144.ft1', '144.fx1', '144.gm1', '216.jz1', '216.kc1', '648.jc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 40327, 269279866800], 'label': '46656.ir.72.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gp1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715401
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cp1', '36.w1', '36.bm1', '36.ce1'], 'contains': ['144.ft1', '144.gc1', '144.gl1', '216.ka1', '216.kd1', '648.je1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6227464327, 269279866800, 39957127], 'label': '46656.ir.72.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gq1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715402
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cq1', '36.bi1'], 'contains': ['144.fu1', '144.gh1', '144.gi1', '216.ke1', '216.kg1', '648.jj1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 269278773445, 1174320, 1481684400, 355419187304], 'label': '46656.ir.72.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '72.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gr1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715403
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cq1', '36.m1', '36.bj1', '36.dr1'], 'contains': ['144.fv1', '144.gj1', '144.gm1', '216.ke1', '216.kg1', '216.kh1', '648.jh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 1481684835, 1174320, 1481684400, 269279866800], 'label': '46656.ir.72.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gs1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715404
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cr1', '36.m1', '36.bm1', '36.do1'], 'contains': ['144.fv1', '144.gk1', '144.gl1', '216.kf1', '216.ki1', '648.ji1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 6267381120, 39366316080, 1481684835, 1174320, 1481684400, 269279866800], 'label': '46656.ir.72.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gt1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715405
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cq1', '36.f1', '36.bk1', '36.dq1'], 'contains': ['144.fw1', '144.gn1', '144.gq1', '216.ke1', '648.jk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 6267381127, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.72.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gu1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715406
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cr1', '36.f1', '36.bl1', '36.dn1'], 'contains': ['144.fw1', '144.go1', '144.gp1', '216.kf1', '648.jl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 6267381120, 39366316080, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.72.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gv1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715407
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cs1', '36.x1', '36.ba1', '36.dr1'], 'contains': ['144.fx1', '144.fz1', '144.gj1', '216.kj1', '216.kl1', '648.jf1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40327, 39366316080, 1481684835, 1174320, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.72.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gw1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715408
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.c1', '6.e1'], 'contains': ['24.f1', '24.h1', '24.bm1', '24.bs1', '24.bv1', '36.g1', '36.v1', '108.ba1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 1134000, 7, 41051299, 325, 269279866800, 1521641624], 'label': '46656.ir.12.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715409
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ct1', '36.x1', '36.bb1', '36.do1'], 'contains': ['144.fx1', '144.gf1', '144.gk1', '216.kk1', '216.km1', '648.jg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267381120, 40327, 39366316080, 1481684835, 1174320, 1481684400, 269279866800], 'label': '46656.ir.72.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.gx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gx1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715410
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cs1', '36.k1', '36.bc1', '36.dq1'], 'contains': ['144.fy1', '144.ga1', '144.gn1', '216.kl1', '648.jm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 40327], 'label': '46656.ir.72.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.gy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gy1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715411
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.gz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ct1', '36.k1', '36.bd1', '36.dn1'], 'contains': ['144.fy1', '144.gg1', '144.go1', '216.km1', '648.jn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267381120, 40327, 39366316080, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.72.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.gz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gz1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715412
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ha1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cu1', '36.x1', '36.bm1', '36.cd1'], 'contains': ['144.fz1', '144.gc1', '144.gk1', '216.kn1', '216.ko1', '648.jo1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 269279866800, 6227827207, 39957127], 'label': '46656.ir.72.ha1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.ha1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ha1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715413
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cu1', '36.k1', '36.bl1', '36.ct1'], 'contains': ['144.ga1', '144.gd1', '144.go1', '216.ko1', '648.jp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 39957127], 'label': '46656.ir.72.hb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.hb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hb1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715414
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cv1', '36.bi1'], 'contains': ['144.gb1', '144.ge1', '144.gh1', '216.kp1', '216.kq1', '648.jr1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6267744007, 39366316080, 269278773445, 1174320, 1481684400, 355419187304, 39957127], 'label': '46656.ir.72.hc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '72.hc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hc1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715415
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cv1', '36.x1', '36.bj1', '36.ce1'], 'contains': ['144.gc1', '144.gf1', '144.gj1', '216.kp1', '216.kq1', '216.kr1', '648.jq1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504, 269279866800, 39957127], 'label': '46656.ir.72.hd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.hd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hd1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715416
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.he1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cv1', '36.k1', '36.bk1', '36.di1'], 'contains': ['144.gd1', '144.gg1', '144.gn1', '216.kp1', '648.js1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504, 39957127, 1174645], 'label': '46656.ir.72.he1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.he1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.he1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715417
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cw1', '36.bo1', '36.di1', '36.dq1'], 'contains': ['144.fs1', '144.gn1', '144.gr1', '216.ks1', '648.jt1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267744000, 41050800, 1481684400, 39957120, 41051125, 1521641624], 'label': '46656.ir.72.hf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.hf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hf1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715418
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1', '36.bn1', '36.dn1', '36.dq1'], 'contains': ['144.fn1', '144.fo1', '144.fw1', '144.fy1', '144.gr1', '216.jv1', '216.kt1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 41051125, 31697930984, 37885034880], 'label': '46656.ir.72.hg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.hg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hg1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715419
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.e1', '6.l1'], 'contains': ['24.f1', '24.i1', '24.bn1', '24.bu1', '24.bw1', '36.h1', '36.t1', '108.bb1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 7, 6227827818, 269279866800], 'label': '46656.ir.12.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715420
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.db1', '36.bp1', '36.ct1', '36.dq1'], 'contains': ['144.ga1', '144.gq1', '144.gr1', '216.ku1', '648.kb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 41051125, 1481684400, 6227827207, 1521641624], 'label': '46656.ir.72.hh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.hh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hh1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715421
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.de1', '36.bp1', '36.di1', '36.dn1'], 'contains': ['144.gg1', '144.gp1', '144.gr1', '216.kv1', '648.ke1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 41051125, 1481684400, 1521641624], 'label': '46656.ir.72.hi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.hi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hi1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715422
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cw1', '24.cx1', '36.bs1', '36.ce1', '36.dr1'], 'contains': ['144.ft1', '144.gj1', '144.gs1', '216.ks1', '216.kw1', '648.kf1'], 'core': '432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6267744000, 1521641624], 'label': '46656.ir.72.hj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.hj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hj1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715423
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cy1', '36.bq1', '36.dp1', '36.ds1'], 'contains': ['144.a1', '216.kx1', '288.dc1', '1944.gx1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.hk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.hk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hk1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715424
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '24.cy1', '36.br1', '36.do1', '36.dr1'], 'contains': ['144.fv1', '144.fx1', '144.gs1', '216.kt1', '216.kx1'], 'core': '432.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39916807, 39366316080, 1521641955, 39957120, 41050800, 1481684400, 269279866800], 'label': '46656.ir.72.hl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '72.hl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hl1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216715425
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cz1', '24.da1', '24.db1', '36.bt1', '36.cd1', '36.dr1'], 'contains': ['144.fz1', '144.gm1', '144.gs1', '216.ku1', '216.ky1', '648.kh1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207, 1521641624], 'label': '46656.ir.72.hm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.hm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hm1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715426
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cz1', '36.bu1', '36.bx1', '36.ds1'], 'contains': ['144.a1', '216.ky1', '288.ck1', '1944.ha1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207, 623823424560], 'label': '46656.ir.72.hn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.hn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hn1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715427
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.ho1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cz1', '24.da1', '36.bv1'], 'contains': ['144.gt1', '216.ky1', '288.cl1', '1944.hb1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207, 463289990028], 'label': '46656.ir.72.ho1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bv1', 'old_label': '72.ho1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ho1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715428
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dc1', '24.dd1', '24.de1', '36.bt1', '36.ce1', '36.do1'], 'contains': ['144.gf1', '144.gl1', '144.gs1', '216.kv1', '216.kz1', '648.ki1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.72.hp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '72.hp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hp1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715429
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dc1', '36.bu1', '36.by1', '36.dp1'], 'contains': ['144.a1', '216.kz1', '288.dw1', '1944.hd1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.72.hq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.hq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hq1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715430
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.d1', '6.l1'], 'contains': ['24.f1', '24.q1', '24.bx1', '24.by1', '24.cm1', '36.i1', '108.bc1', '108.bm1'], 'core': '48.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 7, 6267381738, 269279866800], 'label': '46656.ir.12.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715431
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '72.hr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dc1', '24.dd1', '36.bv1'], 'contains': ['144.gt1', '216.kz1', '288.dx1', '1944.he1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6267744007, 462923481264, 39366316080, 39957120, 41050800, 1481684400, 269279866800], 'label': '46656.ir.72.hr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bv1', 'old_label': '72.hr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.hr1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715432
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '27.a1', '27.b1'], 'contains': ['162.e1', '162.f1', '162.g1', '162.h1', '162.i1', '162.j1', '162.k1', '162.l1', '162.o1', '162.p1', '162.q1', '162.bd1', '162.be1', '162.bf1', '162.bg1', '729.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 39916800, 6227827207, 499, 7, 41051125], 'label': '46656.ir.81.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715433
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '27.c1'], 'contains': ['162.a1', '162.b1', '162.c1', '162.d1', '162.s1', '162.t1', '162.u1', '162.v1', '162.w1', '162.x1', '162.y1', '162.z1', '162.ba1', '162.bb1', '162.bc1', '729.a1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [41050800, 1481684400, 39957120, 39916800, 499, 1521641964, 269279866800, 443609999724], 'label': '46656.ir.81.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '81.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 216715434
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1', '48.e1', '48.o1', '48.r1', '48.s1', '48.v1', '48.w1', '48.x1', '48.y1'], 'contains': ['192.a1', '288.h1', '288.k1', '288.l1', '288.m1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.96.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': ['24.c1', '48.a1', '48.b1', '48.c1'], 'normal_contains': ['192.a1', '2592.a1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '1728.47869'}
  • id: 216715435
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': ['486.s1', '486.u1', '486.v1', '486.t1'], 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '48.a1', '48.g1', '48.bf1', '48.bq1', '48.bt1'], 'contains': ['192.a1', '288.be1', '288.bf1', '288.bg1', '288.bh1'], 'core': '96.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.96.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': ['24.a1', '48.a1'], 'normal_contains': ['192.a1', '864.a1'], 'normalizer': '1.a1', 'old_label': '96.b1', 'projective_image': '46656.ir', 'quotient_action_image': '96.186', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '5184.og'}
  • id: 216715436
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['486.s1', '486.u1', '486.v1', '486.t1'], 'conjugacy_class_count': 1, 'contained_in': ['32.f1', '48.a1', '48.j1', '48.bi1', '48.bv1', '48.ch1'], 'contains': ['192.a1', '288.de1', '288.df1', '288.dg1', '288.dh1', '288.di1', '288.dj1', '288.dk1'], 'core': '96.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 41091127], 'label': '46656.ir.96.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1', 'normal_contained_in': ['24.d1', '48.a1'], 'normal_contains': ['192.a1'], 'normalizer': '1.a1', 'old_label': '96.c1', 'projective_image': '46656.ir', 'quotient_action_image': '96.186', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '96.c1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715437
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '48.f1', '48.g1', '48.h1', '48.i1', '48.j1', '48.k1'], 'contains': ['192.a1', '288.a1', '288.b1', '288.c1', '288.d1', '288.e1', '288.f1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 39916800, 269279866800], 'label': '46656.ir.96.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1', 'subgroup_fusion': None, 'weyl_group': '192.1103'}
  • id: 216715438
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ba1', '32.a1', '48.l1', '48.m1', '48.n1'], 'contains': ['192.b1', '288.g1', '288.h1', '288.i1', '288.j1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [624190336641, 39366316080, 7, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.96.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '96.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715439
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.p1', '48.q1', '48.t1', '48.z1', '48.ba1', '48.bb1', '48.bc1'], 'contains': ['192.f1', '288.i1', '288.m1', '288.n1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [40323593624, 7, 325, 270715782960, 40323593520, 461482882830], 'label': '46656.ir.96.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '96.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715440
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.u1', '48.bd1', '48.be1'], 'contains': ['192.g1', '288.j1', '288.m1', '288.o1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [40323593624, 195088320270, 7, 325, 270715782960, 40323593520], 'label': '46656.ir.96.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.m1', 'old_label': '96.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1', 'subgroup_fusion': None, 'weyl_group': '1944.3491'}
  • id: 216715441
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1'], 'contains': ['24.l1', '24.m1', '24.p1', '24.ci1', '24.cj1', '24.co1', '24.cp1', '36.j1', '36.w1', '108.bn1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6267381127, 39957127, 269279866800], 'label': '46656.ir.12.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715442
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '48.f1', '48.o1', '48.bf1', '48.bg1', '48.bh1', '48.bi1', '48.bj1'], 'contains': ['192.a1', '288.p1', '288.q1', '288.r1', '288.s1', '288.t1', '288.u1', '288.v1', '288.w1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827200], 'label': '46656.ir.96.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 216715443
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cl1', '32.b1', '48.l1', '48.bl1', '48.bm1'], 'contains': ['192.b1', '288.s1', '288.y1', '288.z1', '288.ba1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [624190336641, 39366316080, 1481684400, 1481684504, 269279866800, 6227827200], 'label': '46656.ir.96.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '96.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216715444
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '48.bn1'], 'contains': ['192.d1', '288.t1', '288.y1', '288.ba1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [195088320270, 325, 1481684504, 270715782960, 40323593520, 6227827200], 'label': '46656.ir.96.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.j1', 'old_label': '96.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216715445
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '48.p1', '48.bk1', '48.bo1'], 'contains': ['192.f1', '288.w1', '288.x1', '288.y1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [40323593624, 325, 270715782960, 40323593520, 6227827200, 461482882830], 'label': '46656.ir.96.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '96.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216715446
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '48.q1', '48.bk1', '48.bp1'], 'contains': ['192.f1', '288.bb1', '288.bc1', '288.bd1', '288.bg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 41091120, 325, 270715782960, 40323593520, 461482882830], 'label': '46656.ir.96.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '96.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216715447
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.x1', '32.c1', '48.m1', '48.bl1', '48.br1'], 'contains': ['192.b1', '288.bc1', '288.bh1', '288.bi1', '288.bj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [41091120, 39366316080, 622713012218, 325, 1481684400, 269279866800], 'label': '46656.ir.96.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '96.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1', 'subgroup_fusion': None, 'weyl_group': '648.299'}
  • id: 216715448
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.y1', '32.c1', '48.bs1'], 'contains': ['192.c1', '288.bd1', '288.bh1', '288.bj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [41091120, 39366316080, 461333739315, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.96.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.k1', 'old_label': '96.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715449
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1', '48.g1', '48.k1', '48.r1', '48.bj1', '48.bu1', '48.bv1', '48.bw1', '48.bx1', '48.by1', '48.bz1', '48.ca1', '48.cb1', '48.cc1', '48.cd1'], 'contains': ['192.a1', '288.bk1', '288.bl1', '288.bm1', '288.bn1', '288.bo1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 325, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.96.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1', 'subgroup_fusion': None, 'weyl_group': '576.8389'}
  • id: 216715450
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1', '48.f1', '48.s1', '48.bf1', '48.bu1', '48.cg1', '48.ch1', '48.cj1'], 'contains': ['192.a1', '288.bp1', '288.bq1', '288.br1', '288.bs1', '288.bt1', '288.by1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6267744000], 'label': '46656.ir.96.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1', 'subgroup_fusion': None, 'weyl_group': '288.950'}
  • id: 216715451
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1', '48.t1', '48.bk1', '48.ci1'], 'contains': ['192.f1', '288.br1', '288.bu1', '288.bw1', '288.bz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 325, 270715782960, 104, 6267744000, 716634334350], 'label': '46656.ir.96.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '96.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1', 'subgroup_fusion': None, 'weyl_group': '432.300'}
  • id: 216715452
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1'], 'contains': ['24.m1', '24.n1', '24.o1', '24.cs1', '24.ct1', '24.cu1', '24.cv1', '36.k1', '36.x1', '108.br1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 39916800, 6227827207, 39957127, 269279866800], 'label': '46656.ir.12.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715453
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1', '48.u1'], 'contains': ['192.g1', '288.br1', '288.bv1', '288.bx1', '288.ca1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 455255499150, 325, 270715782960, 104, 6267744000], 'label': '46656.ir.96.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '96.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1', 'subgroup_fusion': None, 'weyl_group': '216.53'}
  • id: 216715454
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cx1', '32.d1', '48.n1', '48.bl1', '48.ck1'], 'contains': ['192.b1', '288.bt1', '288.bu1', '288.bv1', '288.cb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 269279866800, 623711294721, 6267744000], 'label': '46656.ir.96.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1', 'old_label': '96.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1', 'subgroup_fusion': None, 'weyl_group': '648.299'}
  • id: 216715455
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '48.h1', '48.bg1', '48.bq1', '48.bv1', '48.bw1', '48.cg1'], 'contains': ['192.a1', '288.cc1', '288.cd1', '288.ce1', '288.cf1', '288.cg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.96.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1', 'subgroup_fusion': None, 'weyl_group': '1728.47045'}
  • id: 216715456
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cz1', '32.e1', '48.l1', '48.br1', '48.ck1'], 'contains': ['192.b1', '288.ci1', '288.ck1', '288.cl1', '288.cm1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 622713415418, 325, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.96.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '96.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715457
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.da1', '32.e1', '48.bs1'], 'contains': ['192.c1', '288.ci1', '288.cl1', '288.cn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 269279866800, 455107081395, 6227827207], 'label': '46656.ir.96.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bs1', 'old_label': '96.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216715458
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1', '48.i1', '48.o1', '48.bh1', '48.bt1', '48.bx1', '48.cg1', '48.ch1'], 'contains': ['192.a1', '288.ch1', '288.ci1', '288.cj1', '288.cp1', '288.cq1', '288.cr1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.96.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715459
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1', '48.p1', '48.bp1', '48.ci1'], 'contains': ['192.f1', '288.cm1', '288.cn1', '288.co1', '288.cr1', '288.cs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [40323593624, 325, 270715782960, 40323593520, 6227827207, 461482882830], 'label': '46656.ir.96.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '96.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715460
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1', '48.j1', '48.r1', '48.bh1', '48.bq1', '48.by1', '48.cj1', '48.cl1', '48.cm1'], 'contains': ['192.a1', '288.ct1', '288.cu1', '288.cv1', '288.cw1', '288.cx1', '288.cy1'], 'core': '192.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 269279866800, 39957127], 'label': '46656.ir.96.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '96.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715461
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cy1', '32.f1', '48.m1', '48.bm1', '48.ck1'], 'contains': ['192.b1', '288.cz1', '288.dc1', '288.dd1', '288.dg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39366316080, 622713012218, 325, 1481684400, 269279866800, 41091127], 'label': '46656.ir.96.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '96.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216715462
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.f1', '48.bn1'], 'contains': ['192.d1', '288.cz1', '288.dd1', '288.dh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [195088320270, 325, 1481684504, 270715782960, 40323593520, 41091127], 'label': '46656.ir.96.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bn1', 'old_label': '96.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1', 'subgroup_fusion': None, 'weyl_group': '972.460'}
  • id: 216715463
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.g1', '6.k1'], 'contains': ['24.r1', '24.s1', '24.v1', '24.bg1', '24.bq1', '24.ci1', '24.cs1', '36.ba1', '36.bc1', '108.n1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 7, 40320, 269279866800], 'label': '46656.ir.12.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715464
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1', '48.q1', '48.bo1', '48.ci1'], 'contains': ['192.f1', '288.cz1', '288.da1', '288.db1', '288.dk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 325, 270715782960, 40323593520, 461482882830, 41091127], 'label': '46656.ir.96.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '96.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715465
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dc1', '32.g1', '48.n1', '48.bm1', '48.br1'], 'contains': ['192.b1', '288.dn1', '288.dp1', '288.dr1', '288.dw1', '288.dx1', '288.dy1', '288.dz1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [6267744007, 39366316080, 622713012218, 325, 1481684400, 269279866800], 'label': '46656.ir.96.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '96.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1', 'subgroup_fusion': None, 'weyl_group': '1944.2344'}
  • id: 216715466
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dd1', '32.g1', '48.bs1'], 'contains': ['192.c1', '288.dn1', '288.dq1', '288.ds1', '288.dx1', '288.ea1', '288.ea2'], 'core': '1728.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6267744007, 39366316080, 456583967628, 325, 1481684400, 269279866800], 'label': '46656.ir.96.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bs1', 'old_label': '96.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1', 'subgroup_fusion': None, 'weyl_group': '972.459'}
  • id: 216715467
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.g1', '48.bn1'], 'contains': ['192.d1', '288.do1', '288.dp1', '288.ds1', '288.dy1', '288.ea1', '288.ea2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [6267744007, 39366316080, 2917600664, 455255499150, 325, 270715782960], 'label': '46656.ir.96.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.bn1', 'old_label': '96.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1', 'subgroup_fusion': None, 'weyl_group': '972.460'}
  • id: 216715468
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.g1'], 'contains': ['192.e1', '288.do1', '288.dq1', '288.dr1', '288.ds1', '288.dz1', '288.ea1', '288.ea2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [6267744007, 1481684725, 39366316080, 455255499150, 270715782960, 104], 'label': '46656.ir.96.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.bf1', 'old_label': '96.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1', 'subgroup_fusion': None, 'weyl_group': '486.185'}
  • id: 216715469
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1', '48.i1', '48.s1', '48.bg1', '48.bi1', '48.bt1', '48.bz1', '48.cj1'], 'contains': ['192.a1', '288.dl1', '288.dm1', '288.dn1', '288.do1', '288.dt1', '288.du1', '288.dv1', '288.eb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6267744007, 39366316080, 325, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.96.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1', 'subgroup_fusion': None, 'weyl_group': '2592.lw'}
  • id: 216715470
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1', '48.t1', '48.bo1', '48.bp1'], 'contains': ['192.f1', '288.dp1', '288.dq1', '288.dv1', '288.ec1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267744007, 39366316080, 325, 270715782960, 104, 716634334350], 'label': '46656.ir.96.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '96.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715471
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1', '48.u1'], 'contains': ['192.g1', '288.dr1', '288.ds1', '288.dv1', '288.ed1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6267744007, 39366316080, 455255499150, 325, 270715782960, 104], 'label': '46656.ir.96.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '96.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216715472
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '36.l1', '54.x1'], 'contains': ['216.b1', '216.c1', '216.q1', '216.u1', '216.y1', '216.fa1', '216.fd1', '216.ff1', '216.im1', '216.it1', '216.jy1', '324.c1', '324.i1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 7, 1174320, 1481684400, 39916800, 6227827207], 'label': '46656.ir.108.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715473
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '36.m1', '54.x1'], 'contains': ['216.c1', '216.z1', '216.ba1', '216.fg1', '216.fh1', '216.ke1', '216.kf1', '324.e1', '972.k1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 39916800, 6267381127, 7], 'label': '46656.ir.108.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715474
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '6.i1', '6.k1'], 'contains': ['24.r1', '24.t1', '24.w1', '24.bo1', '24.bt1', '24.co1', '24.ct1', '36.bb1', '36.bd1', '108.o1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 7, 269279866800, 40320], 'label': '46656.ir.12.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715475
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.n1', '54.a1'], 'contains': ['216.d1', '216.l1', '216.m1', '216.fs1', '216.ft1', '216.ho1', '216.hp1', '324.j1', '972.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 39916800, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.108.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 216715476
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.o1', '54.a1'], 'contains': ['216.d1', '216.n1', '216.o1', '216.fu1', '216.fv1', '216.hq1', '216.hr1', '324.k1', '972.b1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174819, 39916800, 6227827207, 7, 104, 325], 'label': '46656.ir.108.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715477
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.p1', '54.a1'], 'contains': ['216.e1', '216.l1', '216.n1', '216.fz1', '216.ga1', '216.hy1', '216.hz1', '324.j1', '972.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 40323593520, 39916800, 6227827207, 499, 7, 325], 'label': '46656.ir.108.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '108.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715478
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.q1', '54.a1'], 'contains': ['216.e1', '216.m1', '216.o1', '216.gb1', '216.gc1', '216.ia1', '216.ib1', '324.k1', '972.d1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1174819, 40323593624, 40323593520, 39916800, 6227827207, 7, 325], 'label': '46656.ir.108.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715479
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.r1', '54.a1'], 'contains': ['216.d1', '216.e1', '216.g1', '216.p1', '216.s1', '216.t1', '216.w1', '216.fl1', '216.fy1', '216.gf1', '216.hd1', '216.ie1', '216.il1', '216.ir1', '216.jo1', '324.i1', '324.l1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 39916800, 1174645, 1174320, 6227827207, 7, 104], 'label': '46656.ir.108.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715480
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '36.u1', '54.r1'], 'contains': ['216.f1', '216.h1', '216.k1', '216.gi1', '216.gj1', '216.he1', '216.hf1', '324.m1', '972.f1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 1134000, 37885034880, 499, 7, 325, 31697930984], 'label': '46656.ir.108.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '108.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715481
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '36.v1', '54.r1'], 'contains': ['216.f1', '216.i1', '216.j1', '216.gj1', '216.gk1', '216.hg1', '216.hh1', '324.o1', '972.g1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 1134000, 37885034880, 7, 41051299, 325, 31697930984], 'label': '46656.ir.108.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '108.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715482
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '36.s1', '54.a1'], 'contains': ['216.g1', '216.l1', '216.o1', '216.go1', '216.gp1', '216.hi1', '216.hj1', '324.m1', '972.h1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [387037284480, 39957120, 499, 7, 325, 39957224, 1134000], 'label': '46656.ir.108.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715483
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1', '36.t1', '54.a1'], 'contains': ['216.g1', '216.m1', '216.n1', '216.gq1', '216.gr1', '216.hk1', '216.hl1', '324.p1', '972.i1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 39916800, 1174645, 1174320, 7, 6227827818, 104], 'label': '46656.ir.108.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715705
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1', '72.ft1'], 'contains': ['288.o1', '288.ca1', '288.ed1', '432.dz1', '432.eo1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [6267744007, 455255499150, 7, 294706903784, 325, 388956924720], 'label': '46656.ir.144.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '144.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.co1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216715484
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.j1', '36.w1', '54.x1'], 'contains': ['216.u1', '216.x1', '216.ba1', '216.ix1', '216.iy1', '216.jz1', '216.ka1', '324.s1', '972.l1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 6267381127, 1481684835, 1174320, 1481684400, 39916800, 39957127], 'label': '46656.ir.108.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715485
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.f1', '6.h1'], 'contains': ['24.g1', '24.h1', '24.r1', '24.bp1', '24.bs1', '36.y1', '36.be1', '108.ca1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 39916800, 499, 7, 325, 269279866800, 1521641624], 'label': '46656.ir.12.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715486
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.k1', '36.x1', '54.x1'], 'contains': ['216.x1', '216.y1', '216.z1', '216.kl1', '216.km1', '216.ko1', '216.kp1', '324.u1', '972.m1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 39916800, 6227827207, 39957127], 'label': '46656.ir.108.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715487
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1', '54.b1', '54.c1', '54.q1'], 'contains': ['216.bb1', '216.bc1', '216.bf1', '216.fw1', '216.gu1', '216.ih1', '216.ji1', '324.v1', '324.x1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 268280812800, 6227827207, 7, 40320], 'label': '46656.ir.108.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216715488
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1', '54.d1', '54.e1', '54.q1'], 'contains': ['216.bb1', '216.bd1', '216.bg1', '216.gs1', '216.gx1', '216.jf1', '216.jj1', '324.w1', '324.y1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174320, 1174645, 6267381127, 268280812800, 7, 40320], 'label': '46656.ir.108.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715489
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '54.b1', '54.d1', '54.r1'], 'contains': ['216.h1', '216.i1', '216.bb1', '216.gt1', '216.gv1', '324.z1', '972.p1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1481684400, 39957120, 39916800, 499, 7, 325, 1521641624], 'label': '46656.ir.108.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715490
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '54.c1', '54.e1', '54.r1'], 'contains': ['216.j1', '216.k1', '216.bb1', '216.gw1', '216.gz1', '324.ba1', '972.q1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1481684400, 39957120, 39916800, 7, 41051299, 325, 1521641624], 'label': '46656.ir.108.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715491
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '54.b1', '54.e1', '54.s1'], 'contains': ['216.bb1', '216.gy1', '216.hb1', '324.bb1', '972.r1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227827818, 355419187304, 40320, 1174645], 'label': '46656.ir.108.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216715492
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '54.c1', '54.d1', '54.s1'], 'contains': ['216.bb1', '216.ha1', '216.hc1', '324.bc1', '972.s1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6267381738, 355419187304, 40320, 1174645], 'label': '46656.ir.108.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715493
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1', '54.q1'], 'contains': ['216.bc1', '216.be1', '216.bg1', '216.ii1', '216.ij1', '216.jk1', '216.jn1', '324.bd1', '324.be1', '324.bf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174320, 1174645, 6267381127, 268280812800, 39957127, 40320], 'label': '46656.ir.108.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715494
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '54.q1'], 'contains': ['216.bd1', '216.be1', '216.bf1', '216.jg1', '216.jh1', '216.jl1', '216.jm1', '324.bg1', '324.bh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 268280812800, 6227827207, 39957127, 40320], 'label': '46656.ir.108.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715495
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ck1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '54.f1'], 'contains': ['216.bh1', '216.bj1', '216.bl1', '216.dr1', '216.ds1', '216.eq1', '216.er1', '324.a1', '324.bi1', '324.bk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 499, 1481684400, 443130957804, 269279866800, 40320, 1481684844], 'label': '46656.ir.108.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '108.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216715496
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['23328.d1', '23328.j1', '23328.a1', '23328.g1', '23328.h1', '23328.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.f1', '4.i1', '6.o1', '8.m1', '18.s1', '54.bj1'], 'core': '2.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 499, 7, 41051125, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.2.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.f1', '4.i1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '46656.ir', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715497
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.g1', '6.i1'], 'contains': ['24.h1', '24.j1', '24.r1', '24.br1', '24.bv1', '36.z1', '36.bf1', '108.cb1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684400, 39957120, 39916800, 7, 41051299, 325, 269279866800, 1521641624], 'label': '46656.ir.12.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715498
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1', '54.f1'], 'contains': ['216.bh1', '216.bl1', '216.bm1', '216.dt1', '216.du1', '216.es1', '216.et1', '324.b1', '324.bj1', '324.bl1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 41051299, 1481684400, 443130957804, 269279866800, 40320, 1481684844], 'label': '46656.ir.108.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '108.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216715499
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '54.f1', '54.g1', '54.y1'], 'contains': ['216.bh1', '216.bi1', '216.cd1', '216.cf1', '216.co1', '216.dq1', '216.dv1', '216.ee1', '216.io1', '216.iv1', '216.kb1', '324.c1', '324.bm1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174320, 39916800, 6227827207, 7, 269279866800], 'label': '46656.ir.108.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715500
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '54.f1', '54.h1', '54.z1'], 'contains': ['216.bi1', '216.bj1', '216.bm1', '216.eb1', '216.ec1', '216.ef1', '216.eh1', '324.d1', '324.bn1', '324.bp1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 499, 1481684400, 1521641964, 269279866800, 1134000], 'label': '46656.ir.108.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715501
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1', '54.h1', '54.i1', '54.y1'], 'contains': ['216.bi1', '216.cp1', '216.cq1', '216.eg1', '216.ej1', '216.kh1', '216.ki1', '324.e1', '972.bf1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174320, 39916800, 6267381127, 7, 269279866800], 'label': '46656.ir.108.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715502
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1', '54.g1', '54.i1', '54.z1'], 'contains': ['216.bi1', '216.bk1', '216.ec1', '216.ei1', '216.el1', '324.f1', '324.bq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 41051299, 1481684400, 1521641964, 269279866800, 1134000], 'label': '46656.ir.108.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715503
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1', '54.f1', '54.i1', '54.ba1'], 'contains': ['216.bi1', '216.bl1', '216.ed1', '216.ek1', '216.em1', '324.g1', '324.bo1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 39916800, 6227827818, 269279866800], 'label': '46656.ir.108.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715504
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '54.g1', '54.h1', '54.ba1'], 'contains': ['216.bi1', '216.ct1', '216.en1', '216.eo1', '216.je1', '324.h1', '972.bi1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 39916800, 6267381738, 269279866800], 'label': '46656.ir.108.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715505
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.l1', '36.r1'], 'contains': ['216.bn1', '216.bo1', '216.bp1', '216.bx1', '216.cb1', '216.ce1', '216.cm1', '216.ex1', '216.ez1', '216.fc1', '216.fe1', '216.ig1', '216.in1', '216.ip1', '216.jq1', '324.i1', '324.bm1', '324.br1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 1174320, 39916800, 6227827207, 435], 'label': '46656.ir.108.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bd1', 'old_label': '108.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216715506
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ec1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1', '36.p1', '54.j1'], 'contains': ['216.br1', '216.bt1', '216.bv1', '216.fm1', '216.fn1', '216.hs1', '216.ht1', '324.j1', '972.ba1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [268280812800, 499, 7, 325, 39916800, 355419187304, 6227827207], 'label': '46656.ir.108.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '108.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715507
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1', '36.q1', '54.j1'], 'contains': ['216.br1', '216.bv1', '216.bw1', '216.fo1', '216.fp1', '216.hu1', '216.hv1', '324.k1', '972.bb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [268280812800, 1174819, 7, 325, 39916800, 355419187304, 6227827207], 'label': '46656.ir.108.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '108.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715508
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1', '6.i1', '6.l1'], 'contains': ['24.r1', '24.bu1', '24.bx1', '36.bg1', '108.r1', '108.cc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6227827818, 40320, 269279866800], 'label': '46656.ir.12.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715509
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '54.j1', '54.k1', '54.q1'], 'contains': ['216.br1', '216.bs1', '216.bz1', '216.ca1', '216.ci1', '216.fj1', '216.fw1', '216.gs1', '216.if1', '216.ii1', '216.jg1', '324.l1', '324.br1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 39916800, 355419187304, 6227827207, 1174645], 'label': '46656.ir.108.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715510
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '54.l1', '54.m1', '54.n1'], 'contains': ['216.cg1', '216.hm1', '216.jr1', '324.bs1', '324.bu1', '432.ef1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 39916800, 7, 41051125, 174452060430], 'label': '46656.ir.108.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715511
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1', '36.u1', '54.j1', '54.o1', '54.r1'], 'contains': ['216.bs1', '216.bt1', '216.bw1', '216.gi1', '216.gk1', '216.gt1', '216.gw1', '324.m1', '972.be1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1481684400, 39957120, 1134000, 499, 7, 325, 1521641624], 'label': '46656.ir.108.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715512
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1', '54.o1', '54.p1', '54.q1'], 'contains': ['216.bs1', '216.cj1', '216.ck1', '216.gu1', '216.gx1', '216.jk1', '216.jl1', '324.n1', '324.bt1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381127, 268280812800, 7, 1174320, 39916800, 355419187304, 1174645], 'label': '46656.ir.108.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715513
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1', '54.k1', '54.p1', '54.r1'], 'contains': ['216.bs1', '216.bu1', '216.gj1', '216.gv1', '216.gz1', '324.o1', '972.bg1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1481684400, 39957120, 1134000, 7, 41051299, 325, 1521641624], 'label': '46656.ir.108.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715514
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1', '54.j1', '54.p1', '54.s1'], 'contains': ['216.bs1', '216.bv1', '216.gl1', '216.gy1', '216.ha1', '324.p1', '972.bh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 39916800, 6227827818, 355419187304, 1174645], 'label': '46656.ir.108.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715515
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '54.k1', '54.o1', '54.s1'], 'contains': ['216.bs1', '216.cr1', '216.hb1', '216.hc1', '216.jd1', '324.q1', '972.bi1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 39916800, 6267381738, 355419187304, 1174645], 'label': '46656.ir.108.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715516
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1', '54.q1'], 'contains': ['216.ca1', '216.ch1', '216.ck1', '216.ih1', '216.ij1', '216.jf1', '216.jh1', '324.r1', '324.bw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267381127, 268280812800, 1174320, 39916800, 355419187304, 39957127, 1174645], 'label': '46656.ir.108.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715517
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '54.l1'], 'contains': ['216.cg1', '216.is1', '216.jp1', '324.bv1', '324.bx1', '432.gj1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 174452060430, 39916800, 6227827200], 'label': '46656.ir.108.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
  • id: 216715518
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1', '54.y1'], 'contains': ['216.cf1', '216.cn1', '216.cq1', '216.iw1', '216.ja1', '216.kc1', '216.kd1', '324.s1', '972.bl1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 39916800, 269279866800, 39957127], 'label': '46656.ir.108.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715519
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1', '6.h1', '6.l1'], 'contains': ['24.r1', '24.bw1', '24.by1', '36.bh1', '108.s1', '108.cd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6267381738, 40320, 269279866800], 'label': '46656.ir.12.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715520
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '54.l1'], 'contains': ['216.cg1', '216.js1', '216.jt1', '324.by1', '324.bz1', '324.ca1', '432.hz1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957120, 41050800, 41051125, 39957224, 174452060430, 39916800, 6227827207], 'label': '46656.ir.108.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715521
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1', '54.q1'], 'contains': ['216.ch1', '216.ci1', '216.cj1', '216.ji1', '216.jj1', '216.jm1', '216.jn1', '324.t1', '324.cb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 1174320, 39916800, 355419187304, 6227827207, 39957127, 1174645], 'label': '46656.ir.108.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.br1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715522
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1', '54.y1'], 'contains': ['216.cn1', '216.co1', '216.cp1', '216.kj1', '216.kk1', '216.kn1', '216.kr1', '324.u1', '972.bq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174320, 39916800, 6227827207, 39957127, 269279866800], 'label': '46656.ir.108.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bs1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715523
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1', '36.be1', '54.r1'], 'contains': ['216.h1', '216.j1', '216.bt1', '216.bu1', '216.cv1', '216.he1', '216.hg1', '324.z1', '972.br1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39957120, 39916800, 37885034880, 499, 7, 325, 31697930984], 'label': '46656.ir.108.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '108.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bt1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715524
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1', '36.bf1', '54.r1'], 'contains': ['216.i1', '216.k1', '216.bu1', '216.bw1', '216.cv1', '216.hf1', '216.hh1', '324.ba1', '972.bs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39957120, 39916800, 37885034880, 7, 41051299, 325, 31697930984], 'label': '46656.ir.108.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.r1', 'old_label': '108.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715525
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bn1', '54.q1', '54.r1', '54.s1'], 'contains': ['216.f1', '216.v1', '216.bb1', '216.be1', '216.bs1', '216.ch1', '216.cv1', '216.cy1', '216.cz1', '216.hn1', '216.jv1', '324.bu1', '324.ce1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050800, 39957120, 39916800, 37885034880, 7, 41051125, 31697930984], 'label': '46656.ir.108.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bv1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715526
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '54.q1'], 'contains': ['216.bc1', '216.bd1', '216.ca1', '216.cj1', '216.cz1', '216.ik1', '216.ju1', '324.bv1', '324.cf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 41051125, 39916800, 6227827200], 'label': '46656.ir.108.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bw1', 'subgroup_fusion': None, 'weyl_group': '96.206'}
  • id: 216715527
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1', '54.q1'], 'contains': ['216.bf1', '216.bg1', '216.ci1', '216.ck1', '216.cz1', '216.jw1', '216.jx1', '324.ca1', '324.cg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 355459144424, 41051125, 39916800, 6227827207], 'label': '46656.ir.108.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bx1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715528
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1', '54.t1', '54.u1', '54.y1'], 'contains': ['216.da1', '216.de1', '216.dk1', '216.dv1', '216.eg1', '216.iw1', '216.kj1', '324.ch1', '972.n1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174320, 6227827207, 7, 269279866800, 40320], 'label': '46656.ir.108.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.by1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715529
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1', '54.v1', '54.w1', '54.y1'], 'contains': ['216.da1', '216.dg1', '216.do1', '216.ee1', '216.ej1', '216.kc1', '216.kk1', '324.ci1', '972.o1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 7, 1174320, 1481684400, 269279866800, 40320], 'label': '46656.ir.108.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715530
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1'], 'contains': ['24.s1', '24.u1', '24.w1', '24.ch1', '24.cj1', '24.cq1', '24.cv1', '36.bi1', '36.bj1', '36.bk1', '108.t1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 39957127, 269279866800, 40320], 'label': '46656.ir.12.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715531
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1', '54.t1', '54.v1', '54.z1'], 'contains': ['216.bj1', '216.bk1', '216.da1', '216.ef1', '216.ei1', '324.cc1', '324.cj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 499, 1481684400, 1521641964, 39916800, 269279866800], 'label': '46656.ir.108.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715532
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1', '54.u1', '54.w1', '54.z1'], 'contains': ['216.bk1', '216.bm1', '216.da1', '216.eh1', '216.el1', '324.cd1', '324.ck1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 41051299, 1481684400, 1521641964, 39916800, 269279866800], 'label': '46656.ir.108.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cb1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715533
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1', '54.t1', '54.w1', '54.ba1'], 'contains': ['216.da1', '216.ek1', '216.en1', '324.cl1', '972.r1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 6227827818, 269279866800, 40320], 'label': '46656.ir.108.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cc1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715534
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1', '54.u1', '54.v1', '54.ba1'], 'contains': ['216.da1', '216.em1', '216.eo1', '324.cm1', '972.s1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 1481684400, 1174320, 6267381738, 269279866800, 40320], 'label': '46656.ir.108.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cd1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715535
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ba1', '36.bc1', '54.x1'], 'contains': ['216.db1', '216.dc1', '216.dl1', '216.fd1', '216.fg1', '216.ix1', '216.kl1', '324.ch1', '972.t1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6227827207, 7, 40320], 'label': '46656.ir.108.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '108.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ce1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715536
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bb1', '36.bd1', '54.x1'], 'contains': ['216.db1', '216.df1', '216.dm1', '216.ff1', '216.fh1', '216.jz1', '216.km1', '324.ci1', '972.u1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 7, 40320], 'label': '46656.ir.108.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715537
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bi1', '36.bj1', '36.bk1', '54.x1'], 'contains': ['216.dc1', '216.dh1', '216.dm1', '216.it1', '216.iy1', '216.ke1', '216.kp1', '324.cn1', '972.v1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6267381127, 39957127, 40320], 'label': '46656.ir.108.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cg1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715538
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bi1', '36.bj1'], 'contains': ['216.dd1', '216.di1', '216.dn1', '216.iu1', '216.iz1', '216.kg1', '216.kq1', '324.cn1', '972.x1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39366316080, 270715783064, 1481684400, 1174320, 6267381127, 39957127, 40320], 'label': '46656.ir.108.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ch1', 'old_label': '108.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ch1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715539
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '54.y1'], 'contains': ['216.de1', '216.dj1', '216.do1', '216.iv1', '216.ja1', '216.kh1', '216.kr1', '324.cn1', '972.w1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 269279866800, 40320, 39957127], 'label': '46656.ir.108.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ci1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715540
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bl1', '36.bm1', '54.x1'], 'contains': ['216.df1', '216.dh1', '216.dl1', '216.jy1', '216.ka1', '216.kf1', '216.ko1', '324.co1', '972.y1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 1174320, 6227827207, 39957127, 40320], 'label': '46656.ir.108.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cj1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715541
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1'], 'contains': ['24.t1', '24.u1', '24.v1', '24.cn1', '24.cp1', '24.cr1', '24.cu1', '36.bl1', '36.bm1', '108.u1'], 'core': '96.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 39957127, 40320, 269279866800], 'label': '46656.ir.12.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715542
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bm1', '54.y1'], 'contains': ['216.dg1', '216.dj1', '216.dk1', '216.kb1', '216.kd1', '216.ki1', '216.kn1', '324.co1', '972.z1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684400, 1174320, 6227827207, 39957127, 269279866800, 40320], 'label': '46656.ir.108.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ck1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715543
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bn1', '36.br1', '54.x1'], 'contains': ['216.c1', '216.x1', '216.bq1', '216.cl1', '216.cu1', '216.cx1', '216.db1', '216.dh1', '216.dp1', '216.fi1', '216.kt1', '324.ce1', '324.cp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 7, 31697931315, 39916800, 37885034880], 'label': '46656.ir.108.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cl1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715544
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bo1', '36.bs1', '54.x1'], 'contains': ['216.u1', '216.z1', '216.dc1', '216.df1', '216.dp1', '216.jb1', '216.ks1', '324.cq1', '972.bk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 6227827200, 1521641624], 'label': '46656.ir.108.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '108.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cm1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715545
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bp1', '36.bt1', '54.x1'], 'contains': ['216.y1', '216.ba1', '216.dl1', '216.dm1', '216.dp1', '216.ku1', '216.kv1', '324.cr1', '972.bn1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 6227827207, 1521641624], 'label': '46656.ir.108.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715546
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bq1', '36.br1', '54.y1', '54.z1', '54.ba1'], 'contains': ['216.a1', '216.bi1', '216.cn1', '216.da1', '216.dj1', '216.ep1', '216.kx1', '324.cp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 7, 269279866800], 'label': '46656.ir.108.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.co1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.co1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715547
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.bs1', '54.y1'], 'contains': ['216.a1', '216.cf1', '216.cp1', '216.de1', '216.dg1', '216.jc1', '216.kw1', '324.cq1', '972.bu1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 6227827200], 'label': '46656.ir.108.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715548
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bt1', '36.bu1', '36.bv1', '54.y1'], 'contains': ['216.a1', '216.co1', '216.cq1', '216.dk1', '216.do1', '216.ky1', '216.kz1', '324.cr1', '972.bv1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.108.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cq1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715549
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1', '36.bw1', '54.f1'], 'contains': ['216.dq1', '216.dr1', '216.du1', '216.eb1', '216.ed1', '216.eq1', '216.es1', '324.cs1', '324.cv1', '324.cx1', '324.cz1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.108.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '108.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cr1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216715550
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1', '54.f1'], 'contains': ['216.dq1', '216.ds1', '216.dt1', '216.ec1', '216.ed1', '216.er1', '216.et1', '324.ct1', '324.cw1', '324.cy1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 39366316080, 41051299, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.108.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '108.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cs1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 216715551
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1', '54.f1', '54.t1', '54.bb1'], 'contains': ['216.dr1', '216.dt1', '216.dv1', '216.ef1', '216.ek1', '324.da1', '324.dc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 499, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.108.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ct1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715552
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.j1'], 'contains': ['24.x1', '24.ba1', '24.cy1', '36.bq1', '36.br1', '48.m1', '324.bs1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 624190336641, 7, 269279866800, 1521641624], 'label': '46656.ir.12.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216715553
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1', '54.f1', '54.u1', '54.bc1'], 'contains': ['216.ds1', '216.du1', '216.dv1', '216.eh1', '216.em1', '324.db1', '324.dd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40819, 39366316080, 41050800, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.108.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cu1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715554
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '54.g1', '54.t1', '54.bc1'], 'contains': ['216.dv1', '216.ei1', '216.en1', '324.de1', '972.cc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39366316080, 41050800, 1481684400, 443130957804, 269279866800, 1481684844], 'label': '46656.ir.108.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cv1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715555
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '54.g1', '54.u1', '54.bb1'], 'contains': ['216.dv1', '216.el1', '216.eo1', '324.df1', '972.ce1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 443130957804, 269279866800, 39957619, 1481684844], 'label': '46656.ir.108.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cw1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715556
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bx1', '36.cd1', '54.y1', '54.bb1', '54.bc1'], 'contains': ['216.dv1', '216.ej1', '216.ep1', '216.ja1', '216.jc1', '216.kn1', '216.ky1', '324.dg1', '972.cf1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 7, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.108.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cx1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715557
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1', '36.bw1'], 'contains': ['216.dw1', '216.dx1', '216.dy1', '216.dz1', '216.ea1', '216.eu1', '216.ev1', '324.cu1', '324.cz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 39366316080, 499, 655477406640, 444, 269279866800, 6227389164], 'label': '46656.ir.108.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.cy1', 'old_label': '108.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cy1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216715558
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1', '54.f1', '54.v1', '54.bd1'], 'contains': ['216.ee1', '216.ef1', '216.em1', '216.eq1', '216.et1', '324.dh1', '324.dj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39366316080, 1481684537, 7, 1174320, 1481684400, 269279866800], 'label': '46656.ir.108.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cz1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715559
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1', '54.f1', '54.w1', '54.be1'], 'contains': ['216.ee1', '216.eh1', '216.ek1', '216.er1', '216.es1', '324.di1', '324.dk1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43633820302, 6267744007, 39366316080, 7, 1174320, 1481684400, 269279866800], 'label': '46656.ir.108.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.da1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715560
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '54.g1', '54.v1', '54.be1'], 'contains': ['216.ee1', '216.ei1', '216.eo1', '324.dl1', '972.cn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39366316080, 43673374222, 7, 1174320, 1481684400, 269279866800], 'label': '46656.ir.108.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.db1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715561
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1', '54.g1', '54.w1', '54.bd1'], 'contains': ['216.ee1', '216.el1', '216.en1', '324.dm1', '972.cp1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1521641657, 6267744007, 39366316080, 7, 1174320, 1481684400, 269279866800], 'label': '46656.ir.108.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dc1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715562
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '54.h1', '54.t1', '54.bd1'], 'contains': ['216.ef1', '216.eg1', '216.en1', '324.dn1', '972.cq1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 1481684537, 7, 1174320, 1481684400, 6227464327, 269279866800], 'label': '46656.ir.108.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dd1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715563
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.k1'], 'contains': ['24.a1', '24.l1', '24.o1', '24.s1', '24.t1', '24.ck1', '24.cw1', '36.bo1', '36.bs1', '108.bw1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6227827200, 41050800, 1481684400, 39957120, 39916800, 41051125, 269279866800, 1521641624], 'label': '46656.ir.12.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1', 'subgroup_fusion': None, 'weyl_group': '1728.46586'}
  • id: 216715564
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '54.h1', '54.v1', '54.bb1'], 'contains': ['216.ef1', '216.ej1', '216.eo1', '324.do1', '972.cr1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 499, 1481684400, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.108.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.de1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715565
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '54.h1', '54.u1', '54.be1'], 'contains': ['216.eg1', '216.eh1', '216.eo1', '324.dp1', '972.ct1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 43673374222, 7, 1174320, 1481684400, 6227464327, 269279866800], 'label': '46656.ir.108.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.df1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715566
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.by1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '54.i1', '54.t1', '54.be1'], 'contains': ['216.eg1', '216.ei1', '216.ek1', '324.dq1', '972.cs1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43633820302, 39366316080, 7, 1174320, 1481684400, 6227464327, 269279866800], 'label': '46656.ir.108.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dg1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715567
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '54.i1', '54.u1', '54.bd1'], 'contains': ['216.eg1', '216.el1', '216.em1', '324.dr1', '972.cu1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1521641657, 39366316080, 7, 1174320, 1481684400, 6227464327, 269279866800], 'label': '46656.ir.108.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dh1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715568
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '54.h1', '54.w1', '54.bc1'], 'contains': ['216.eh1', '216.ej1', '216.en1', '324.ds1', '972.cw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40819, 39366316080, 41050800, 1481684400, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.108.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.di1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715569
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '54.i1', '54.v1', '54.bc1'], 'contains': ['216.ei1', '216.ej1', '216.em1', '324.dt1', '972.cv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 39366316080, 41050800, 1481684400, 269279866800, 443609999724, 1481684844], 'label': '46656.ir.108.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dj1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715570
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '54.i1', '54.w1', '54.bb1'], 'contains': ['216.ej1', '216.ek1', '216.el1', '324.du1', '972.cx1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 269279866800, 443609999724, 39957619, 1481684844], 'label': '46656.ir.108.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dk1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715571
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.by1', '36.ce1', '54.y1', '54.bd1', '54.be1'], 'contains': ['216.ee1', '216.eg1', '216.ep1', '216.kd1', '216.kr1', '216.kw1', '216.kz1', '324.dv1', '972.df1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 39366316080, 39957120, 41050800, 7, 1481684400, 269279866800], 'label': '46656.ir.108.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dl1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715572
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '36.bz1', '54.z1', '54.bb1', '54.bd1'], 'contains': ['216.ef1', '216.el1', '216.ep1', '324.dw1'], 'core': '432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 499, 1481684400, 1521641964, 269279866800], 'label': '46656.ir.108.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dm1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715573
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '36.ca1', '54.z1', '54.bc1', '54.be1'], 'contains': ['216.eh1', '216.ei1', '216.ep1', '324.dx1'], 'core': '432.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39917299, 39366316080, 39957120, 41050800, 1481684400, 1521641964, 269279866800], 'label': '46656.ir.108.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dn1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715574
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.j1'], 'contains': ['24.x1', '24.cl1', '24.cx1', '36.a1', '36.bs1', '48.bl1', '324.bx1'], 'core': '36.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 6227827200, 41050800, 1481684400, 39957120, 39916800, 622713012218, 41051125, 269279866800], 'label': '46656.ir.12.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216715575
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1', '36.cb1', '54.ba1', '54.bb1', '54.be1'], 'contains': ['216.ek1', '216.eo1', '216.ep1', '324.dy1', '972.di1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 1481684400, 39957120, 6227827818, 269279866800], 'label': '46656.ir.108.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.do1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715576
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1', '36.cc1', '54.ba1', '54.bc1', '54.bd1'], 'contains': ['216.em1', '216.en1', '216.ep1', '324.dz1', '972.dj1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39366316080, 469, 41050800, 1481684400, 39957120, 6267744618, 269279866800], 'label': '46656.ir.108.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dp1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715577
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cd1', '36.ct1', '54.x1'], 'contains': ['216.fd1', '216.fh1', '216.fi1', '216.iy1', '216.jb1', '216.ko1', '216.ku1', '324.dg1', '972.dk1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 41050800, 7, 1481684400, 6227827207], 'label': '46656.ir.108.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dq1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715578
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.ce1', '36.di1', '54.x1'], 'contains': ['216.ff1', '216.fg1', '216.fi1', '216.ka1', '216.kp1', '216.ks1', '216.kv1', '324.dv1', '972.dl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [6267744007, 39366316080, 1521641955, 39957120, 41050800, 7, 1481684400], 'label': '46656.ir.108.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dr1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715579
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cf1', '36.ci1', '54.j1'], 'contains': ['216.fj1', '216.fm1', '216.fp1', '216.gi1', '216.gl1', '216.hs1', '216.hu1', '324.ee1', '972.bw1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 268280812800, 499, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.108.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '108.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ds1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715580
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cg1', '36.cj1', '54.j1'], 'contains': ['216.fj1', '216.fn1', '216.fo1', '216.gk1', '216.gl1', '216.ht1', '216.hv1', '324.ef1', '972.bx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [41091120, 268280812800, 1174819, 7, 325, 355419187304, 6227827207], 'label': '46656.ir.108.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '108.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dt1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715581
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cf1', '36.ch1', '36.cm1'], 'contains': ['216.fk1', '216.fq1', '216.fr1', '216.gm1', '216.gn1', '216.hw1', '216.hx1', '324.ee1', '972.by1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 6227827207, 387999647384, 499, 7, 325, 387999647280], 'label': '46656.ir.108.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.du1', 'old_label': '108.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.du1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715582
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cf1', '36.ck1', '54.a1'], 'contains': ['216.fl1', '216.fs1', '216.fv1', '216.go1', '216.gq1', '216.hy1', '216.ia1', '324.ee1', '972.bz1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 41091120, 6227827207, 499, 7, 104, 325], 'label': '46656.ir.108.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dv1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715583
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cg1', '36.cl1', '54.a1'], 'contains': ['216.fl1', '216.ft1', '216.fu1', '216.gp1', '216.gr1', '216.hz1', '216.ib1', '324.ef1', '972.ca1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174819, 41091120, 6227827207, 7, 104, 325], 'label': '46656.ir.108.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dw1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715584
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.du1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '54.b1', '54.j1', '54.bf1'], 'contains': ['216.fm1', '216.fo1', '216.fw1', '216.gt1', '216.gy1', '324.eg1', '972.cb1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 268280812800, 6227827207, 499, 7], 'label': '46656.ir.108.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dx1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715585
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.j1'], 'contains': ['24.x1', '24.cz1', '24.dc1', '36.bt1', '36.bu1', '36.bv1', '48.br1', '324.by1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 622713012218, 6227827207, 41051125, 269279866800], 'label': '46656.ir.12.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216715586
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1', '54.b1', '54.k1', '54.bg1'], 'contains': ['216.fw1', '216.gv1', '216.hb1', '324.ei1', '972.cc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40819, 268280812800, 7, 1174320, 355419187304, 6227827207, 1174645], 'label': '46656.ir.108.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dy1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216715587
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.co1', '54.c1', '54.j1', '54.bg1'], 'contains': ['216.fn1', '216.fp1', '216.fw1', '216.gw1', '216.ha1', '324.eh1', '972.cd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 268280812800, 7, 1174320, 355419187304, 6227827207, 1174645], 'label': '46656.ir.108.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.dz1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715588
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1', '54.c1', '54.k1', '54.bf1'], 'contains': ['216.fw1', '216.gz1', '216.hc1', '324.ej1', '972.ce1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174645, 1174320, 268280812800, 6227827207, 7, 39957619], 'label': '46656.ir.108.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ea1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715589
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1', '54.q1', '54.bf1', '54.bg1'], 'contains': ['216.fw1', '216.gx1', '216.hn1', '216.ij1', '216.ik1', '216.jm1', '216.jw1', '324.ea1', '324.ek1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39957120, 268280812800, 6227827207, 7, 41051125], 'label': '46656.ir.108.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eb1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715590
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '36.ch1'], 'contains': ['216.fx1', '216.gd1', '216.ge1', '216.gg1', '216.gh1', '216.ic1', '216.id1', '324.ee1', '972.cg1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [41091120, 6227827207, 499, 7, 104, 174452060430, 325], 'label': '46656.ir.108.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.ec1', 'old_label': '108.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ec1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715591
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ci1', '36.ck1', '36.cm1', '54.a1'], 'contains': ['216.fy1', '216.fz1', '216.gc1', '216.go1', '216.gr1', '216.ho1', '216.hq1', '324.ee1', '972.ch1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091120, 499, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.108.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ed1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715592
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cj1', '36.cl1', '54.a1'], 'contains': ['216.fy1', '216.ga1', '216.gb1', '216.gp1', '216.gq1', '216.hp1', '216.hr1', '324.ef1', '972.ci1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [40323593624, 41091120, 1174819, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.108.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ee1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715725
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.df1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '48.z1', '48.bd1', '72.dq1', '72.eg1', '72.fl1'], 'contains': ['288.m1', '432.ez1', '432.fd1', '1296.dw1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 499, 7, 325, 269279866800, 104], 'label': '46656.ir.144.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '144.df1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.df1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715593
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '36.cp1', '54.a1'], 'contains': ['216.fs1', '216.fu1', '216.fz1', '216.gb1', '216.gf1', '216.hi1', '216.hk1', '324.eg1', '972.cj1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 6227827207, 499, 7, 104], 'label': '46656.ir.108.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '108.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ef1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715594
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.co1', '36.cq1', '54.a1'], 'contains': ['216.ft1', '216.fv1', '216.ga1', '216.gc1', '216.gf1', '216.hj1', '216.hl1', '324.eh1', '972.ck1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 1174645, 1174320, 6227827207, 7, 39917299, 104], 'label': '46656.ir.108.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eg1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715595
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '54.l1', '54.bh1', '54.bi1'], 'contains': ['216.hm1', '216.is1', '216.js1', '324.eb1', '324.ek1', '432.ee1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 6227827207, 7, 41051125, 174452060430], 'label': '46656.ir.108.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eh1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715596
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1'], 'contains': ['24.y1', '24.da1', '24.dd1', '36.bt1', '36.bv1', '48.bs1', '324.bz1'], 'core': '216.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 463289990028, 41050800, 1481684400, 39957120, 39916800, 6227827207, 41051125, 269279866800], 'label': '46656.ir.12.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.z1', 'old_label': '12.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1', 'subgroup_fusion': None, 'weyl_group': '3888.bx'}
  • id: 216715597
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cu1', '54.d1', '54.j1', '54.bl1'], 'contains': ['216.gs1', '216.gt1', '216.ha1', '216.hs1', '216.hv1', '324.el1', '972.cm1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 499, 7, 1174320, 355419187304, 1174645], 'label': '46656.ir.108.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ei1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715598
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1', '54.d1', '54.k1', '54.bm1'], 'contains': ['216.gs1', '216.gv1', '216.hc1', '324.en1', '972.cn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320, 6267381738, 355419187304, 1174645], 'label': '46656.ir.108.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ej1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715599
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.v1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1', '54.e1', '54.j1', '54.bm1'], 'contains': ['216.gs1', '216.gw1', '216.gy1', '216.ht1', '216.hu1', '324.em1', '972.co1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320, 6227827818, 355419187304, 1174645], 'label': '46656.ir.108.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ek1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715600
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1', '54.e1', '54.k1', '54.bl1'], 'contains': ['216.gs1', '216.gz1', '216.hb1', '324.eo1', '972.cp1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 268280812800, 7, 1174320, 355419187304, 39957619, 1174645], 'label': '46656.ir.108.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.el1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715601
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.fh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1', '54.b1', '54.o1', '54.bl1'], 'contains': ['216.gt1', '216.gu1', '216.hb1', '324.ep1', '972.cq1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 499, 7, 1174320, 6227464327, 355419187304, 1174645], 'label': '46656.ir.108.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.em1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715602
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1', '54.d1', '54.o1', '54.bf1'], 'contains': ['216.gt1', '216.gx1', '216.hc1', '324.eq1', '972.cr1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174320, 1174645, 6267381127, 268280812800, 499, 7], 'label': '46656.ir.108.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.en1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715603
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1', '54.b1', '54.p1', '54.bm1'], 'contains': ['216.gu1', '216.gv1', '216.gy1', '324.es1', '972.cs1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 6227827818, 355419187304, 1174645], 'label': '46656.ir.108.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eo1', 'subgroup_fusion': None, 'weyl_group': '288.1039'}
  • id: 216715604
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1', '54.c1', '54.o1', '54.bm1'], 'contains': ['216.gu1', '216.gw1', '216.hc1', '324.er1', '972.ct1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 6267381738, 355419187304, 1174645], 'label': '46656.ir.108.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ep1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715605
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1', '54.c1', '54.p1', '54.bl1'], 'contains': ['216.gu1', '216.gz1', '216.ha1', '324.et1', '972.cu1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [268280812800, 7, 1174320, 6227464327, 355419187304, 39957619, 1174645], 'label': '46656.ir.108.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eq1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715606
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '54.d1', '54.p1', '54.bg1'], 'contains': ['216.gv1', '216.gx1', '216.ha1', '324.ev1', '972.cv1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [40819, 6267381127, 268280812800, 7, 1174320, 355419187304, 1174645], 'label': '46656.ir.108.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.er1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715607
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '2.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': ['23328.d1', '23328.j1', '23328.a1', '23328.g1', '23328.h1', '23328.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.g1', '4.h1', '6.p1', '8.n1', '18.t1', '54.bk1'], 'core': '2.g1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 6267744007, 41050800, 1481684400, 39957120, 7, 41051125, 6227827818, 269279866800, 461482882830, 1521641624], 'label': '46656.ir.2.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.g1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '46656.ir', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1', 'subgroup_fusion': None, 'weyl_group': '46656.ir'}
  • id: 216715608
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.k1'], 'contains': ['24.a1', '24.n1', '24.p1', '24.v1', '24.w1', '24.db1', '24.de1', '36.bp1', '36.bt1', '108.bx1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 41051125, 269279866800, 1521641624], 'label': '46656.ir.12.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715609
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '54.e1', '54.o1', '54.bg1'], 'contains': ['216.gw1', '216.gx1', '216.hb1', '324.eu1', '972.cw1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39917299, 6267381127, 268280812800, 7, 1174320, 355419187304, 1174645], 'label': '46656.ir.108.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.es1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715610
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '54.e1', '54.p1', '54.bf1'], 'contains': ['216.gx1', '216.gy1', '216.gz1', '324.ew1', '972.cx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355419187304, 1174320, 1174645, 6267381127, 268280812800, 7, 39957619], 'label': '46656.ir.108.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.et1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715611
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cu1', '36.cw1', '54.a1'], 'contains': ['216.hd1', '216.hi1', '216.hl1', '216.ho1', '216.hr1', '216.hy1', '216.ib1', '324.el1', '972.cy1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [39366316080, 6267744007, 1174645, 1174320, 499, 7, 104], 'label': '46656.ir.108.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.eu1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715612
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cv1', '36.cx1', '54.a1'], 'contains': ['216.hd1', '216.hj1', '216.hk1', '216.hp1', '216.hq1', '216.hz1', '216.ia1', '324.em1', '972.cz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1174320, 6227827818, 104, 1174645], 'label': '46656.ir.108.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ev1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 216715613
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '54.l1', '54.bj1', '54.bk1'], 'contains': ['216.hm1', '216.jp1', '216.jt1', '324.ec1', '324.ex1', '432.eq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 6267744007, 41050800, 39957120, 7, 41051125, 174452060430], 'label': '46656.ir.108.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ew1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715614
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1', '54.m1', '54.bh1', '54.bj1'], 'contains': ['216.hm1', '324.ey1', '432.fl1', '972.db1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 499, 7, 41051125, 174452060430], 'label': '46656.ir.108.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ex1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715615
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '54.m1', '54.bi1', '54.bk1'], 'contains': ['216.hm1', '324.ez1', '432.fn1', '972.dc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 7, 41051125, 39917299, 174452060430], 'label': '46656.ir.108.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ey1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715616
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1', '54.n1', '54.bh1', '54.bk1'], 'contains': ['216.hm1', '324.fa1', '432.fm1', '972.dd1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 7, 41051125, 6227827818, 174452060430], 'label': '46656.ir.108.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ez1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715617
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1', '54.n1', '54.bi1', '54.bj1'], 'contains': ['216.hm1', '324.fb1', '432.fo1', '972.de1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39957224, 41050800, 39957120, 6267744618, 7, 41051125, 174452060430], 'label': '46656.ir.108.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fa1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715618
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bx1', '54.q1', '54.bl1', '54.bm1'], 'contains': ['216.gs1', '216.gu1', '216.hn1', '216.jh1', '216.jn1', '216.ju1', '216.jx1', '324.ed1', '324.ex1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [6267744007, 355459144424, 41050800, 39957120, 268280812800, 7, 41051125], 'label': '46656.ir.108.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fb1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715619
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.j1'], 'contains': ['24.ba1', '24.cl1', '24.cz1', '36.bx1', '36.cd1', '48.l1', '324.eb1'], 'core': '72.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [624190336641, 39366316080, 39957120, 41050800, 7, 1481684400, 269279866800, 6227827207, 1521641624], 'label': '46656.ir.12.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216715620
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dj1', '54.r1', '54.bf1', '54.bl1'], 'contains': ['216.gt1', '216.gz1', '216.he1', '216.hh1', '216.hn1', '324.ey1', '972.dg1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050800, 39957120, 37885034880, 499, 7, 41051125, 31697930984], 'label': '46656.ir.108.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fc1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715621
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dk1', '54.r1', '54.bg1', '54.bm1'], 'contains': ['216.gv1', '216.gw1', '216.hf1', '216.hg1', '216.hn1', '324.ez1', '972.dh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [41050800, 39957120, 37885034880, 7, 41051125, 39917299, 31697930984], 'label': '46656.ir.108.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fd1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715622
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1', '54.s1', '54.bf1', '54.bm1'], 'contains': ['216.gy1', '216.hc1', '216.hn1', '324.fa1', '972.di1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39957120, 268280812800, 7, 41051125, 6227827818], 'label': '46656.ir.108.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fe1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715623
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1', '54.s1', '54.bg1', '54.bl1'], 'contains': ['216.ha1', '216.hb1', '216.hn1', '324.fb1', '972.dj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [355459144424, 41050800, 39957120, 6267744618, 268280812800, 7, 41051125], 'label': '46656.ir.108.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ff1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715624
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1', '54.q1'], 'contains': ['216.ih1', '216.ii1', '216.ik1', '216.jj1', '216.jl1', '216.jv1', '216.jx1', '324.fc1', '324.fd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 355459144424, 41051125, 6227827200], 'label': '46656.ir.108.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fg1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715625
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1', '54.l1'], 'contains': ['216.is1', '216.jr1', '216.jt1', '324.fc1', '324.fe1', '432.he1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 41051125, 39957224, 174452060430, 6227827200], 'label': '46656.ir.108.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fh1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715626
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dn1', '36.do1', '54.x1'], 'contains': ['216.it1', '216.ix1', '216.jb1', '216.kf1', '216.km1', '216.kt1', '216.kv1', '324.ff1', '972.dm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 39366316080, 1521641955, 39957120, 41050800, 1481684400, 6227827200], 'label': '46656.ir.108.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fi1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715627
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.do1', '36.dp1', '54.y1'], 'contains': ['216.iv1', '216.iw1', '216.jc1', '216.ki1', '216.kk1', '216.kx1', '216.kz1', '324.ff1', '972.dn1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.108.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fj1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715628
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1', '54.l1'], 'contains': ['216.jp1', '216.jr1', '216.js1', '324.fg1', '324.fh1', '432.lo1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39957120, 41050800, 41051125, 39957224, 174452060430, 6227827207], 'label': '46656.ir.108.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fk1', 'subgroup_fusion': None, 'weyl_group': '864.4668'}
  • id: 216715629
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1', '54.q1'], 'contains': ['216.jf1', '216.jg1', '216.ji1', '216.jk1', '216.ju1', '216.jv1', '216.jw1', '324.fg1', '324.fi1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 41050800, 355459144424, 41051125, 6227827207], 'label': '46656.ir.108.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '108.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fl1', 'subgroup_fusion': None, 'weyl_group': '864.4698'}
  • id: 216715630
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.j1'], 'contains': ['24.ba1', '24.cx1', '24.dc1', '36.by1', '36.ce1', '48.n1', '324.ec1'], 'core': '72.c1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [624190336641, 6267744007, 39366316080, 39957120, 41050800, 7, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.12.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '12.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216715631
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.dq1', '36.dr1', '54.x1'], 'contains': ['216.jy1', '216.jz1', '216.ke1', '216.kl1', '216.ks1', '216.kt1', '216.ku1', '324.fj1', '972.dp1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39916807, 39366316080, 1521641955, 39957120, 41050800, 1481684400, 6227827207], 'label': '46656.ir.108.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1', 'old_label': '108.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fm1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715632
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '108.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dr1', '36.ds1', '54.y1'], 'contains': ['216.kb1', '216.kc1', '216.kh1', '216.kj1', '216.kw1', '216.kx1', '216.ky1', '324.fj1', '972.dr1'], 'core': '432.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 41050800, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.108.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.fn1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
  • id: 216715633
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': ['324.j1', '324.k1', '324.ee1', '324.ef1'], 'conjugacy_class_count': 1, 'contained_in': ['48.ce1', '72.a1', '72.b1', '72.c1', '72.cp1', '72.hk1', '72.hn1', '72.hq1'], 'contains': ['432.a1', '576.p1', '3888.fv1'], 'core': '144.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.144.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': ['16.a1', '72.a1', '72.b1', '72.c1'], 'normal_contains': ['432.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '46656.ir', 'quotient_action_image': '4.2', 'quotient_action_kernel': '36.9', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715634
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '72.d1', '72.e1', '72.f1', '72.g1', '72.h1', '72.i1', '72.bq1'], 'contains': ['288.a1', '288.l1', '288.ce1', '432.b1', '432.c1', '432.d1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 39916800], 'label': '46656.ir.144.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.b1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '288.936'}
  • id: 216715635
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '72.d1', '72.j1', '72.k1'], 'contains': ['288.a1', '288.v1', '288.bq1', '432.e1', '432.f1', '432.g1', '432.h1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 39916800, 6227827200], 'label': '46656.ir.144.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.c1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216715636
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '72.e1', '72.k1', '72.l1', '72.m1', '72.n1', '72.o1', '72.ch1'], 'contains': ['288.a1', '288.bf1', '288.bo1', '432.i1', '432.j1', '432.k1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 325, 1134000, 31697930984, 37885034880], 'label': '46656.ir.144.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.d1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715637
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1', '72.l1', '72.bq1', '72.br1'], 'contains': ['288.a1', '288.cg1', '288.cx1', '432.l1', '432.m1', '432.n1', '432.o1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [325, 1481684400, 1481684504, 269279866800, 40320, 39957127], 'label': '46656.ir.144.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.e1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715638
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1', '72.d1', '72.j1', '72.m1'], 'contains': ['288.a1', '288.cq1', '288.du1', '432.p1', '432.q1', '432.r1', '432.s1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 39916800, 6227827207], 'label': '46656.ir.144.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.f1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715639
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '72.e1', '72.j1', '72.p1', '72.br1'], 'contains': ['288.a1', '288.cy1', '288.dj1', '432.t1', '432.u1', '432.v1', '432.w1', '432.x1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 325, 1134000, 31658054504, 39957127, 37885034880], 'label': '46656.ir.144.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.g1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715640
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.m1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.e1', '72.q1', '72.r1', '72.bs1'], 'contains': ['288.d1', '288.h1', '288.cd1', '432.b1', '432.z1', '432.ba1', '432.bb1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 7, 1481684400, 39916800, 269279866800], 'label': '46656.ir.144.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.h1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1', 'subgroup_fusion': None, 'weyl_group': '288.958'}
  • id: 216715641
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1', '6.b1'], 'contains': ['24.b1', '24.bb1', '24.bc1', '24.bf1', '24.bn1', '24.bz1', '24.cb1', '36.cf1', '36.ci1', '36.ck1', '36.cm1', '108.cr1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 41091120, 1481684400, 6227827207, 499, 7, 325, 269279866800], 'label': '46656.ir.12.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216715642
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '72.s1', '72.t1', '72.u1', '72.w1', '72.x1', '72.y1', '72.z1'], 'contains': ['288.e1', '288.k1', '288.cf1', '432.d1', '432.ba1', '432.bc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 325, 39916800, 104], 'label': '46656.ir.144.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.i1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715643
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1', '72.v1', '72.ba1', '72.bb1', '72.bc1', '72.bd1', '72.bq1', '72.bt1'], 'contains': ['288.f1', '288.l1', '288.cg1', '432.c1', '432.bb1', '432.bc1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 7, 325, 39916800, 31658054504, 37885034880], 'label': '46656.ir.144.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '144.j1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715644
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '72.s1', '72.be1', '72.bi1'], 'contains': ['288.e1', '288.p1', '288.bp1', '432.e1', '432.bd1', '432.be1', '432.bf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 39916800, 6227827200, 104], 'label': '46656.ir.144.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.k1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216715645
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.f1', '72.bf1'], 'contains': ['288.b1', '288.q1', '288.bs1', '432.g1', '432.be1', '432.bg1', '432.bh1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [40323593624, 268280812800, 39916800, 40323593520, 6227827200, 34096648645], 'label': '46656.ir.144.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.k1', 'old_label': '144.l1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 216715646
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.s1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.f1', '72.q1', '72.bg1', '72.bj1'], 'contains': ['288.d1', '288.s1', '288.bt1', '432.f1', '432.bd1', '432.bg1', '432.bh1', '432.bi1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 39916800, 269279866800, 6227827200], 'label': '46656.ir.144.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '144.m1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216715647
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1', '72.t1', '72.bh1', '72.bi1'], 'contains': ['288.e1', '288.u1', '288.by1', '432.h1', '432.bf1', '432.bg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 39916800, 40323593520, 6227827200], 'label': '46656.ir.144.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.n1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715648
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '72.u1', '72.bi1', '72.bl1'], 'contains': ['288.e1', '288.be1', '288.bk1', '432.j1', '432.bj1', '432.bk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.144.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.o1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715649
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1', '72.v1', '72.bk1', '72.ch1'], 'contains': ['288.f1', '288.bf1', '288.bl1', '432.i1', '432.bj1', '432.bl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 325, 1481684400, 1134000, 1521641624], 'label': '46656.ir.144.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.p1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715650
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.g1', '72.r1', '72.bj1', '72.bm1', '72.bn1', '72.bo1', '72.bp1', '72.ci1'], 'contains': ['288.d1', '288.bh1', '288.bn1', '432.k1', '432.bk1', '432.bl1', '432.bm1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 1481684400, 269279866800, 1134000], 'label': '46656.ir.144.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.q1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715651
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.h1', '72.bz1'], 'contains': ['288.c1', '288.cc1', '288.cu1', '432.l1', '432.bn1', '432.bo1', '432.bq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 1481684400, 355419187304, 40320, 39957127, 269279867125], 'label': '46656.ir.144.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '144.r1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216715652
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.bb1', '24.bd1', '24.be1', '24.bm1', '24.bn1', '24.ca1', '24.cc1', '36.cg1', '36.cj1', '36.cl1', '108.cs1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 1481684504, 1174819, 41091120, 1481684400, 6227827207, 7, 325, 269279866800], 'label': '46656.ir.12.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1', 'subgroup_fusion': None, 'weyl_group': '7776.kl'}
  • id: 216715653
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.h1', '72.bm1', '72.bs1', '72.ca1'], 'contains': ['288.d1', '288.cd1', '288.cv1', '432.m1', '432.bn1', '432.bo1', '432.bp1', '432.br1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 269279866800, 40320, 39957127], 'label': '46656.ir.144.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.br1', 'old_label': '144.s1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216715654
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1', '72.bk1', '72.bq1', '72.cb1'], 'contains': ['288.f1', '288.ce1', '288.cx1', '432.n1', '432.bn1', '432.bs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 40320, 39957127], 'label': '46656.ir.144.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.t1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715655
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1', '72.bk1', '72.br1', '72.bt1'], 'contains': ['288.f1', '288.cg1', '288.cy1', '432.o1', '432.bq1', '432.br1', '432.bs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [268280812800, 325, 31658054504, 40320, 39957127, 37885034880], 'label': '46656.ir.144.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '144.u1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715656
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.i1', '72.bf1'], 'contains': ['288.b1', '288.ch1', '288.dl1', '432.q1', '432.bt1', '432.bu1', '432.bx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684725, 39366316080, 268280812800, 39916800, 6227827207, 104], 'label': '46656.ir.144.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '144.v1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216715657
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.i1', '72.q1', '72.bg1', '72.bn1'], 'contains': ['288.d1', '288.ci1', '288.dn1', '432.p1', '432.bt1', '432.bu1', '432.bv1', '432.bw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 39916800, 269279866800, 6227827207], 'label': '46656.ir.144.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.w1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216715658
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1', '72.s1', '72.bh1', '72.bl1'], 'contains': ['288.e1', '288.cj1', '288.dt1', '432.r1', '432.bt1', '432.by1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 39916800, 6227827207, 104], 'label': '46656.ir.144.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.x1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715659
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1', '72.t1', '72.be1', '72.bl1'], 'contains': ['288.e1', '288.cp1', '288.eb1', '432.s1', '432.bw1', '432.bx1', '432.by1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 39916800, 40323593520, 6227827207], 'label': '46656.ir.144.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.y1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715660
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '72.bf1'], 'contains': ['288.b1', '288.ct1', '288.de1', '432.v1', '432.bz1', '432.ca1', '432.cb1', '432.ce1', '432.cf1', '432.cf2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [40323593624, 301891126320, 1481684400, 1134000, 39957127, 34096648645], 'label': '46656.ir.144.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '144.z1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216715661
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '72.bz1'], 'contains': ['288.c1', '288.cu1', '288.df1', '432.t1', '432.ca1', '432.cb1', '432.cc1', '432.cf1', '432.cf2', '432.cg1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 1481684400, 1134000, 355419187304, 39957127, 269279867125], 'label': '46656.ir.144.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bz1', 'old_label': '144.ba1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216715662
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.j1', '72.r1', '72.bg1', '72.ca1'], 'contains': ['288.d1', '288.cv1', '288.dg1', '432.u1', '432.bz1', '432.cc1', '432.ce1', '432.cg1', '432.ch1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1481684400, 269279866800, 1134000, 39957127], 'label': '46656.ir.144.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.bb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715663
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.f1', '6.m1'], 'contains': ['24.bc1', '24.be1', '24.bg1', '24.bp1', '24.bu1', '36.cn1', '36.cp1', '108.ct1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 499, 7, 269279866800], 'label': '46656.ir.12.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715664
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '72.u1', '72.be1', '72.bh1'], 'contains': ['288.e1', '288.cw1', '288.di1', '432.x1', '432.bz1', '432.ca1', '432.cd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 325, 1481684400, 1481684504, 1134000, 39957127], 'label': '46656.ir.144.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.bc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715665
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1', '72.v1', '72.br1', '72.cb1'], 'contains': ['288.f1', '288.cx1', '288.dj1', '432.w1', '432.cb1', '432.cc1', '432.cd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 1134000, 39957127], 'label': '46656.ir.144.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.bd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715666
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1', '72.bq1', '72.br1', '72.ch1'], 'contains': ['288.a1', '288.f1', '288.bl1', '432.y1', '432.ci1', '432.cj1', '432.ck1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 325, 1481684400, 39916800, 1521641624], 'label': '46656.ir.144.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.be1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216715667
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.k1', '72.bu1', '72.bz1', '72.ce1'], 'contains': ['288.c1', '288.bm1', '432.ci1', '432.cl1', '432.cm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [268280812800, 39957120, 325, 39916800, 37885034880, 1521641624], 'label': '46656.ir.144.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '144.bf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715668
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.k1', '72.bs1', '72.bv1', '72.by1', '72.ca1', '72.cc1', '72.cf1', '72.ci1'], 'contains': ['288.d1', '288.bn1', '432.cj1', '432.cl1', '432.cm1', '432.cn1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 39957120, 1481684400, 39916800, 269279866800, 1521641624], 'label': '46656.ir.144.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 216715669
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1', '72.bt1', '72.bw1', '72.bx1', '72.cb1', '72.cd1', '72.cg1', '72.ch1'], 'contains': ['288.f1', '288.bo1', '432.ck1', '432.cl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 39957120, 325, 39916800, 31697930984, 37885034880], 'label': '46656.ir.144.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715670
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bx1', '48.l1', '72.ck1', '72.cl1', '72.cm1'], 'contains': ['288.g1', '288.z1', '288.ck1', '432.co1', '432.cp1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 624302466480, 7, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.144.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216715671
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bq1', '48.m1', '72.ck1', '72.cn1', '72.co1'], 'contains': ['288.g1', '288.bi1', '288.dc1', '432.cq1', '432.cr1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.144.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715672
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.by1', '48.n1', '72.ck1', '72.cq1', '72.cr1'], 'contains': ['288.g1', '288.cb1', '288.dw1', '432.ct1', '432.cu1', '432.cv1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.144.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715673
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '36.bz1', '72.cl1', '72.cn1', '72.cq1'], 'contains': ['288.g1', '432.cw1', '432.dc1', '432.dg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 2917601004, 499, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.144.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216715674
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.g1', '6.n1'], 'contains': ['24.bd1', '24.bf1', '24.bg1', '24.br1', '24.bw1', '36.co1', '36.cq1', '108.cu1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 7, 39917299, 269279866800], 'label': '46656.ir.12.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715675
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.cg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1', '36.cb1', '72.cl1', '72.co1', '72.cr1'], 'contains': ['288.g1', '432.cy1', '432.dd1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [469, 39366316080, 624302466480, 1481684400, 6227827818, 269279866800], 'label': '46656.ir.144.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 216715676
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '36.ca1', '72.cm1', '72.cn1', '72.cr1'], 'contains': ['288.g1', '432.cz1', '432.de1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091619, 39366316080, 2917601004, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.144.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715677
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '36.cc1', '72.cm1', '72.co1', '72.cq1'], 'contains': ['288.g1', '432.db1', '432.df1', '432.dh1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [469, 39366316080, 6267744618, 1481684400, 269279866800, 623823424560], 'label': '46656.ir.144.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715678
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.l1', '48.o1', '72.q1', '72.cs1', '72.ct1'], 'contains': ['288.h1', '288.s1', '288.ci1', '432.co1', '432.di1', '432.dj1', '432.dk1', '432.dl1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 7, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.144.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
  • id: 216715679
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.l1', '48.p1', '72.cu1'], 'contains': ['288.i1', '288.y1', '288.cm1', '432.cp1', '432.dl1', '432.dm1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [554365249658, 40323593520, 6227827207, 7, 325, 269279866800], 'label': '46656.ir.144.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.z1', 'old_label': '144.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715680
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.m1', '48.q1', '72.cu1'], 'contains': ['288.i1', '288.bc1', '288.cz1', '432.cq1', '432.dn1', '432.dq1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 641394472778, 270715782960], 'label': '46656.ir.144.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '144.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715681
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.a1', '48.m1', '72.r1', '72.cs1'], 'contains': ['288.h1', '288.bh1', '288.dg1', '432.cr1', '432.do1', '432.dp1', '432.dq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.144.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1', 'old_label': '144.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1', 'subgroup_fusion': None, 'weyl_group': '7776.be'}
  • id: 216715682
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.r1', '72.r1', '72.bs1', '72.ct1', '72.cv1', '72.cw1', '72.cx1', '72.cy1'], 'contains': ['288.h1', '288.bn1', '288.cv1', '432.cs1', '432.dr1', '432.ds1', '432.dt1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.144.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715683
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n1', '48.s1', '72.q1', '72.cs1', '72.cv1'], 'contains': ['288.h1', '288.bt1', '288.dn1', '432.ct1', '432.du1', '432.dv1', '432.dw1', '432.dx1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.144.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.bu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216715684
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n1', '48.t1', '72.cu1'], 'contains': ['288.i1', '288.bu1', '288.dp1', '432.cu1', '432.dw1', '432.dy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 270715782960, 623711294721, 104], 'label': '46656.ir.144.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '144.bv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715685
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.f1', '6.n1'], 'contains': ['24.bg1', '24.bs1', '24.bx1', '36.cr1', '108.cv1', '108.dy1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6227827207, 40819, 7, 269279866800], 'label': '46656.ir.12.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715686
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n1', '48.u1'], 'contains': ['288.j1', '288.bv1', '288.dr1', '432.cv1', '432.dw1', '432.dz1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [6267744007, 39366316080, 622713012218, 7, 325, 270715782960], 'label': '46656.ir.144.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.bw1', 'old_label': '144.bw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 216715726
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1', '48.ba1', '72.dq1', '72.eh1', '72.fm1'], 'contains': ['288.m1', '432.fa1', '432.fg1', '1296.dx1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 40323593520, 7, 6227827818, 325, 269279866800], 'label': '46656.ir.144.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '144.dg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dg1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715687
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1', '72.s1', '72.cz1', '72.da1', '72.db1', '72.dc1', '72.dd1', '72.du1'], 'contains': ['288.k1', '288.p1', '288.cj1', '432.di1', '432.ea1', '432.eb1', '432.ec1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 325, 6227827207, 104], 'label': '46656.ir.144.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.bx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715688
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1', '72.t1', '72.df1', '72.di1', '72.dj1', '72.dk1', '72.dl1', '72.du1'], 'contains': ['288.k1', '288.u1', '288.cp1', '432.dj1', '432.ea1', '432.ed1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 7, 325, 40323593520, 6227827207], 'label': '46656.ir.144.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.by1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715689
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1', '72.d1', '72.dg1', '72.dm1', '72.dn1', '72.do1', '72.dp1', '72.dv1'], 'contains': ['288.l1', '288.v1', '288.cq1', '432.dk1', '432.ec1', '432.ed1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.144.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.bz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715690
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1', '48.p1', '72.dh1', '72.dq1', '72.dr1'], 'contains': ['288.m1', '288.w1', '288.cr1', '432.dl1', '432.eb1', '432.ed1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [40323593624, 7, 325, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.144.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bd1', 'old_label': '144.ca1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715691
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '72.de1', '72.ds1', '72.dt1'], 'contains': ['288.n1', '288.x1', '288.cs1', '432.dm1', '432.eb1', '432.ee1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [300933848880, 7, 325, 382729979624, 6227827207, 461482882830], 'label': '46656.ir.144.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.cb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715692
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1', '72.de1', '72.dw1', '72.dx1'], 'contains': ['288.n1', '288.bb1', '288.db1', '432.dn1', '432.ef1', '432.eh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 300933848880, 7, 325, 382729979624, 457175461950], 'label': '46656.ir.144.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.cc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715693
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '72.u1', '72.cz1', '72.df1', '72.dy1', '72.dz1', '72.ea1', '72.eb1'], 'contains': ['288.k1', '288.be1', '288.di1', '432.do1', '432.eg1', '432.eh1', '432.ei1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 7, 325, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.144.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.cd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715694
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '72.e1', '72.v1', '72.dg1', '72.ec1', '72.ed1', '72.ee1', '72.ef1'], 'contains': ['288.l1', '288.bf1', '288.dj1', '432.dp1', '432.eg1', '432.ei1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 268280812800, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.144.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.ce1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ce1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715695
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '48.q1', '72.dh1', '72.eg1', '72.eh1'], 'contains': ['288.m1', '288.bg1', '288.dk1', '432.dq1', '432.eh1', '432.ei1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091120, 39366316080, 7, 325, 269279866800, 104], 'label': '46656.ir.144.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '144.cf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cf1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715696
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.g1', '6.m1'], 'contains': ['24.bg1', '24.bv1', '24.by1', '36.cs1', '108.cw1', '108.ea1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 6227827207, 7, 39957619, 269279866800], 'label': '46656.ir.12.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715697
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '72.u1', '72.du1', '72.ei1', '72.ej1', '72.ek1', '72.el1', '72.em1'], 'contains': ['288.k1', '288.bk1', '288.cw1', '432.dr1', '432.ej1', '432.el1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 7, 325, 1481684400, 1521641624], 'label': '46656.ir.144.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.cg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cg1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715698
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '72.v1', '72.bq1', '72.en1', '72.eo1', '72.ep1', '72.eq1', '72.fc1'], 'contains': ['288.l1', '288.bl1', '288.cx1', '432.ds1', '432.ej1', '432.ek1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 7, 325, 1481684400, 1521641624], 'label': '46656.ir.144.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.ch1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ch1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715699
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1', '72.e1', '72.bt1', '72.dv1', '72.er1', '72.es1', '72.et1', '72.eu1', '72.ev1', '72.ew1', '72.ex1', '72.ey1', '72.ez1', '72.fa1', '72.fb1', '72.fc1'], 'contains': ['288.l1', '288.bo1', '288.cy1', '432.dt1', '432.ek1', '432.el1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 39957120, 7, 325, 31697930984, 37885034880], 'label': '46656.ir.144.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.ci1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715700
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1', '72.s1', '72.df1', '72.ei1', '72.fd1', '72.fe1', '72.ff1', '72.fg1'], 'contains': ['288.k1', '288.bp1', '288.dt1', '432.du1', '432.em1', '432.en1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 7, 325, 104], 'label': '46656.ir.144.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.cj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cj1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715701
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1', '72.d1', '72.dg1', '72.er1', '72.fh1', '72.fi1', '72.fj1', '72.fk1'], 'contains': ['288.l1', '288.bq1', '288.du1', '432.dv1', '432.em1', '432.ep1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 1481684400, 1481684504], 'label': '46656.ir.144.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.ck1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ck1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715702
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1', '48.t1', '48.u1', '72.dh1', '72.fl1', '72.fm1'], 'contains': ['288.m1', '288.br1', '288.dv1', '432.dw1', '432.em1', '432.eo1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 7, 325, 269279866800, 104], 'label': '46656.ir.144.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '144.cl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cl1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715703
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1', '72.t1', '72.cz1', '72.ei1', '72.fn1', '72.fo1', '72.fp1', '72.fq1'], 'contains': ['288.k1', '288.by1', '288.eb1', '432.dx1', '432.en1', '432.eo1', '432.ep1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 6267744007, 268280812800, 7, 325, 40323593520], 'label': '46656.ir.144.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.cm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cm1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715704
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1', '72.de1', '72.fr1', '72.fs1'], 'contains': ['288.n1', '288.bz1', '288.ec1', '432.dy1', '432.eo1', '432.eq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267744007, 388956924720, 7, 294706903784, 325, 174451657230], 'label': '46656.ir.144.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '144.cn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cn1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715706
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bu1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '72.w1', '72.da1', '72.di1', '72.dy1', '72.ej1', '72.fd1', '72.fn1'], 'contains': ['288.k1', '432.er1', '432.ez1', '432.fd1', '1296.dg1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [499, 7, 325, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.144.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.cp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cp1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715707
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.k1', '6.m1', '6.n1'], 'contains': ['24.c1', '24.bg1', '24.bt1', '24.cj1', '24.ck1', '24.cu1', '24.db1', '36.cd1', '36.ct1', '108.eb1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 6227827207, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.12.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715708
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1', '72.w1', '72.db1', '72.dj1', '72.dz1', '72.ek1', '72.fe1', '72.fo1'], 'contains': ['288.k1', '432.et1', '432.fe1', '1296.dh1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39917299, 39366316080, 268280812800, 7, 325, 104], 'label': '46656.ir.144.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.cq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cq1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715709
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1', '72.x1', '72.da1', '72.dk1', '72.ea1', '72.el1', '72.fe1', '72.fp1'], 'contains': ['288.k1', '432.eu1', '432.fa1', '432.ff1', '1296.di1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 7, 325, 6227827818, 104], 'label': '46656.ir.144.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.cr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cr1', 'subgroup_fusion': None, 'weyl_group': '144.191'}
  • id: 216715710
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.bm1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1', '72.y1', '72.dc1', '72.di1', '72.eb1', '72.el1', '72.ff1', '72.fo1'], 'contains': ['288.k1', '432.eu1', '432.fg1', '1296.dj1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 7, 325, 6227827818, 40323593520], 'label': '46656.ir.144.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.cs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cs1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715711
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '72.z1', '72.dd1', '72.dl1', '72.dy1', '72.ek1', '72.ff1', '72.fp1'], 'contains': ['288.k1', '432.ev1', '432.fb1', '432.fh1', '1296.dk1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091619, 7, 325, 269279866800, 31658054504, 37885034880], 'label': '46656.ir.144.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.ct1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ct1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715712
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1', '72.z1', '72.dc1', '72.dk1', '72.dz1', '72.ej1', '72.fg1', '72.fq1'], 'contains': ['288.k1', '432.ew1', '432.fi1', '1296.dl1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 7, 325, 1481684400, 1481684504, 39957619], 'label': '46656.ir.144.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.cu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cu1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715713
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1', '72.x1', '72.db1', '72.dl1', '72.eb1', '72.em1', '72.fd1', '72.fq1'], 'contains': ['288.k1', '432.ey1', '432.fj1', '1296.dm1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 6267744618, 7, 325, 104], 'label': '46656.ir.144.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.cv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cv1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715714
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1', '72.y1', '72.dd1', '72.dj1', '72.ea1', '72.em1', '72.fg1', '72.fn1'], 'contains': ['288.k1', '432.ey1', '432.fc1', '432.fk1', '1296.dn1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 268280812800, 6267744618, 7, 325, 40323593520], 'label': '46656.ir.144.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.cw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cw1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715715
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1', '72.f1', '72.ba1', '72.dm1', '72.ec1', '72.en1', '72.es1', '72.fh1'], 'contains': ['288.l1', '432.er1', '432.fd1', '1296.do1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 499, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.144.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.cx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cx1', 'subgroup_fusion': None, 'weyl_group': '288.936'}
  • id: 216715716
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1', '72.f1', '72.bb1', '72.dn1', '72.ed1', '72.ep1', '72.eu1', '72.fi1'], 'contains': ['288.l1', '432.es1', '432.fe1', '1296.dp1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39917299, 39366316080, 7, 325, 1481684400, 1481684504], 'label': '46656.ir.144.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.cy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cy1', 'subgroup_fusion': None, 'weyl_group': '288.936'}
  • id: 216715717
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.cz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1', '72.g1', '72.ba1', '72.bc1', '72.ee1', '72.eo1', '72.ep1', '72.ev1'], 'contains': ['288.l1', '432.es1', '432.et1', '1296.dq1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39917299, 268280812800, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.144.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '144.cz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cz1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715718
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '6.e1', '6.f1', '6.g1', '6.h1', '6.i1', '6.k1', '6.l1', '6.m1', '6.n1', '6.o1', '6.p1', '9.a1', '27.b1', '27.c1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 41050800, 1481684400, 39957120, 39916800, 6227827207, 499, 7, 41051125, 269279866800, 1521641624], 'label': '46656.ir.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715719
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1'], 'contains': ['24.bh1', '24.bi1', '24.bj1', '24.bk1', '24.bl1', '24.cd1', '24.ce1', '36.ch1', '36.cm1', '108.cy1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [270715782960, 40323593624, 41091120, 40323593520, 6227827207, 499, 7, 325, 461482882830], 'label': '46656.ir.12.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '12.bk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715720
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.da1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1', '72.h1', '72.dm1', '72.do1', '72.ef1', '72.ex1', '72.fi1', '72.fj1'], 'contains': ['288.l1', '432.ff1', '432.fg1', '1296.dr1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 6227827818], 'label': '46656.ir.144.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.da1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.da1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715721
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.db1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '72.i1', '72.bd1', '72.dp1', '72.ec1', '72.eo1', '72.eu1', '72.fj1'], 'contains': ['288.l1', '432.ev1', '432.fh1', '1296.ds1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091619, 268280812800, 7, 325, 31658054504, 37885034880], 'label': '46656.ir.144.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.db1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.db1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715722
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1', '72.g1', '72.bb1', '72.bd1', '72.ee1', '72.en1', '72.eq1', '72.ey1'], 'contains': ['288.l1', '432.ew1', '432.ex1', '1296.dt1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 7, 325, 1481684400, 1481684504, 39957619], 'label': '46656.ir.144.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.dc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dc1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715723
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.x1', '72.i1', '72.bc1', '72.do1', '72.ed1', '72.eq1', '72.es1', '72.fk1'], 'contains': ['288.l1', '432.ex1', '432.fi1', '1296.du1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [268280812800, 7, 325, 31658054504, 39957619, 37885034880], 'label': '46656.ir.144.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.dd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dd1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715724
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.de1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1', '72.h1', '72.dn1', '72.dp1', '72.ef1', '72.ez1', '72.fh1', '72.fk1'], 'contains': ['288.l1', '432.fj1', '432.fk1', '1296.dv1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 6267744618, 7, 325], 'label': '46656.ir.144.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.de1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.de1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715727
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '48.bb1', '72.dr1', '72.eg1', '72.fm1'], 'contains': ['288.m1', '432.fb1', '432.fh1', '1296.dy1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [41091619, 39366316080, 7, 325, 269279866800, 104], 'label': '46656.ir.144.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '144.dh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dh1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715728
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.di1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.y1', '48.bc1', '48.be1', '72.dr1', '72.eh1', '72.fl1'], 'contains': ['288.m1', '432.fc1', '432.fj1', '1296.dz1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 6267744618, 7, 325, 269279866800, 104], 'label': '46656.ir.144.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '144.di1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.di1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715729
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1', '72.ds1', '72.dw1', '72.fr1'], 'contains': ['288.n1', '432.ez1', '432.fl1', '1296.ea1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [300933848880, 499, 7, 325, 382729979624, 461482882830], 'label': '46656.ir.144.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '144.dj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dj1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715730
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.h1', '6.o1'], 'contains': ['24.bo1', '24.bp1', '24.bw1', '24.bz1', '24.cc1', '36.cu1', '36.cw1', '108.cz1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 1174320, 1174645, 499, 7, 269279866800], 'label': '46656.ir.12.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715731
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ba1', '72.ds1', '72.dx1', '72.fs1'], 'contains': ['288.n1', '432.fa1', '432.fm1', '1296.eb1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [300933848880, 7, 325, 6227827818, 382729979624, 461482882830], 'label': '46656.ir.144.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.dk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dk1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715732
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1', '72.dt1', '72.dw1', '72.fs1'], 'contains': ['288.n1', '432.fb1', '432.fn1', '1296.ec1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091619, 300933848880, 7, 325, 382729979624, 457175461950], 'label': '46656.ir.144.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.dl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dl1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715733
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1', '72.dt1', '72.dx1', '72.fr1'], 'contains': ['288.n1', '432.fc1', '432.fo1', '1296.ed1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [388956924720, 6267744618, 7, 294706903784, 325, 174451657230], 'label': '46656.ir.144.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1', 'old_label': '144.dm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dm1', 'subgroup_fusion': None, 'weyl_group': '3888.il'}
  • id: 216715734
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bd1', '72.ft1'], 'contains': ['288.o1', '432.ez1', '1296.ee1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [300933848880, 499, 7, 325, 382729979624, 176887030590], 'label': '46656.ir.144.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '144.dn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dn1', 'subgroup_fusion': None, 'weyl_group': '216.168'}
  • id: 216715735
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.do1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.be1', '72.ft1'], 'contains': ['288.o1', '432.fc1', '1296.ef1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [388956924720, 6267744618, 7, 455255499150, 294706903784, 325], 'label': '46656.ir.144.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.cf1', 'old_label': '144.do1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.do1', 'subgroup_fusion': None, 'weyl_group': '1944.3484'}
  • id: 216715736
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1', '72.bi1', '72.cz1', '72.fu1'], 'contains': ['288.p1', '288.be1', '288.by1', '432.fp1', '432.fq1', '432.fr1', '432.fs1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 325, 6227827200, 104], 'label': '46656.ir.144.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.dp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dp1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715737
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1', '72.s1', '72.fu1', '72.fy1'], 'contains': ['288.p1', '288.cf1', '288.dt1', '432.ft1', '432.fu1', '432.fv1', '432.fw1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 325, 6227827200, 104], 'label': '46656.ir.144.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.dq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dq1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715738
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1', '72.be1', '72.du1', '72.fu1'], 'contains': ['288.p1', '288.cp1', '288.cw1', '432.fx1', '432.fy1', '432.fz1', '432.ga1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 1174327, 268280812800, 325, 40323593520, 6227827207], 'label': '46656.ir.144.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.dr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dr1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715739
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ds1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1', '72.be1', '72.cz1', '72.fy1'], 'contains': ['288.p1', '288.di1', '288.eb1', '432.gb1', '432.gc1', '432.gd1', '432.ge1', '432.gf1', '432.gg1', '432.gh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 325, 6227827200, 104, 41091127], 'label': '46656.ir.144.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.ds1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ds1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715740
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bk1', '72.de1'], 'contains': ['288.x1', '288.bb1', '288.bz1', '432.fq1', '432.gj1', '432.gl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 300933848880, 325, 6227827200, 382729979624, 457175461950], 'label': '46656.ir.144.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.dt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dt1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715741
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.i1', '6.p1'], 'contains': ['24.bo1', '24.br1', '24.bu1', '24.ca1', '24.cb1', '36.cv1', '36.cx1', '108.da1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 1174320, 1174645, 7, 6227827818, 269279866800], 'label': '46656.ir.12.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715742
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.du1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1', '72.bi1', '72.df1', '72.fw1'], 'contains': ['288.u1', '288.be1', '288.bp1', '432.fp1', '432.gk1', '432.gm1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091120, 268280812800, 325, 40323593520, 6227827200], 'label': '46656.ir.144.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.du1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.du1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715743
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1', '72.k1', '72.dg1', '72.fv1'], 'contains': ['288.v1', '288.bf1', '288.bq1', '432.fr1', '432.gk1', '432.gn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 6227827200], 'label': '46656.ir.144.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.dv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dv1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715744
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bf1', '48.bk1', '72.dh1'], 'contains': ['288.w1', '288.bg1', '288.br1', '432.fq1', '432.gk1', '432.go1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 41091120, 325, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.144.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '144.dw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dw1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715745
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bf1', '48.bl1', '72.bj1', '72.cs1', '72.fx1'], 'contains': ['288.s1', '288.bh1', '288.bt1', '432.fs1', '432.gm1', '432.gn1', '432.go1', '432.gp1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 1481684504, 269279866800, 6227827200], 'label': '46656.ir.144.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1', 'old_label': '144.dx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dx1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216715746
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bg1', '72.fz1'], 'contains': ['288.r1', '288.cc1', '288.dm1', '432.fu1', '432.gq1', '432.gr1', '432.gu1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684400, 6227827200, 355419187304, 269279867125], 'label': '46656.ir.144.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fz1', 'old_label': '144.dy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dy1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216715747
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.dz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bg1', '72.q1', '72.fx1', '72.ga1'], 'contains': ['288.s1', '288.cd1', '288.dn1', '432.ft1', '432.gq1', '432.gr1', '432.gs1', '432.gt1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39916807, 39366316080, 1481684835, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.144.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.dz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dz1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216715748
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1', '72.d1', '72.fv1', '72.gb1'], 'contains': ['288.v1', '288.ce1', '288.du1', '432.fv1', '432.gq1', '432.gv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 1481684400, 1481684504, 6227827200], 'label': '46656.ir.144.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.ea1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715749
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.eb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bg1', '72.t1', '72.fw1', '72.fy1'], 'contains': ['288.u1', '288.cf1', '288.eb1', '432.fw1', '432.gt1', '432.gu1', '432.gv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [40323593624, 39916807, 268280812800, 325, 40323593520, 6227827200], 'label': '46656.ir.144.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.eb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eb1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715750
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ec1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bh1', '72.bf1'], 'contains': ['288.q1', '288.ch1', '288.ct1', '432.fy1', '432.gw1', '432.gx1', '432.ha1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1481684725, 1174327, 39366316080, 268280812800, 6227827207, 104], 'label': '46656.ir.144.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '144.ec1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ec1', 'subgroup_fusion': None, 'weyl_group': '216.171'}
  • id: 216715751
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bh1', '72.bg1', '72.ct1', '72.fx1'], 'contains': ['288.s1', '288.ci1', '288.cv1', '432.fx1', '432.gw1', '432.gx1', '432.gy1', '432.gz1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1174327, 39366316080, 1481684835, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.144.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.ed1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1', 'subgroup_fusion': None, 'weyl_group': '432.759'}
  • id: 216715752
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.h1', '6.p1'], 'contains': ['24.bo1', '24.bs1', '24.by1', '36.cy1', '108.db1', '108.ej1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 1174320, 1174645, 7, 6267381738, 269279866800], 'label': '46656.ir.12.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715753
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ee1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1', '72.bh1', '72.du1', '72.fw1'], 'contains': ['288.u1', '288.cj1', '288.cw1', '432.fz1', '432.gw1', '432.hb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1174327, 39366316080, 268280812800, 325, 6227827207, 104], 'label': '46656.ir.144.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.ee1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ee1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715754
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ef1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1', '72.j1', '72.dv1', '72.fv1'], 'contains': ['288.v1', '288.cq1', '288.cy1', '432.ga1', '432.gz1', '432.ha1', '432.hb1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1174327, 39366316080, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.144.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.ef1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ef1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715755
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.eg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1', '72.de1'], 'contains': ['288.x1', '288.db1', '288.ec1', '432.gg1', '432.hc1', '432.hd1', '432.he1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [300933848880, 325, 6227827200, 382729979624, 457175461950, 41091127], 'label': '46656.ir.144.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.eg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eg1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715756
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.eh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bi1', '72.bf1'], 'contains': ['288.q1', '288.de1', '288.dl1', '432.gc1', '432.hf1', '432.hj1', '432.hk1', '432.hm1', '432.hq1', '432.hq2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [268280812800, 325, 1481684504, 40323593520, 6227827200, 41091127], 'label': '46656.ir.144.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bf1', 'old_label': '144.eh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eh1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216715757
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ei1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bi1', '72.fz1'], 'contains': ['288.r1', '288.df1', '288.dm1', '432.ge1', '432.hg1', '432.hi1', '432.hk1', '432.hn1', '432.hq1', '432.hq2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39366316080, 1481684400, 6227827200, 355419187304, 41091127, 269279867125], 'label': '46656.ir.144.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.fz1', 'old_label': '144.ei1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ei1', 'subgroup_fusion': None, 'weyl_group': '648.732'}
  • id: 216715758
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ej1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bi1', '48.bm1', '72.bg1', '72.cs1', '72.ga1'], 'contains': ['288.s1', '288.dg1', '288.dn1', '432.gb1', '432.hf1', '432.hg1', '432.hh1', '432.hm1', '432.hn1', '432.ho1', '432.hp1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 1481684400, 1481684504, 269279866800, 6227827200, 41091127], 'label': '46656.ir.144.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.ej1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ej1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 216715759
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ek1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bi1', '48.bn1'], 'contains': ['288.t1', '288.dh1', '288.do1', '432.gd1', '432.hh1', '432.hi1', '432.hj1', '432.hk1', '432.hp1', '432.hq1', '432.hq2'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [40323593624, 40323593520, 269279866800, 6227827200, 34096648645, 41091127], 'label': '46656.ir.144.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ek1', 'old_label': '144.ek1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ek1', 'subgroup_fusion': None, 'weyl_group': '324.168'}
  • id: 216715760
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.el1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1', '72.bh1', '72.df1', '72.fy1'], 'contains': ['288.u1', '288.di1', '288.dt1', '432.gf1', '432.hf1', '432.hi1', '432.hl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 268280812800, 325, 40323593520, 6227827200, 41091127], 'label': '46656.ir.144.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.el1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.el1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715761
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.em1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1', '72.j1', '72.dg1', '72.gb1'], 'contains': ['288.v1', '288.dj1', '288.du1', '432.gh1', '432.hg1', '432.hj1', '432.hl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 325, 1481684400, 1481684504, 6227827200, 41091127], 'label': '46656.ir.144.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.em1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.em1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715762
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.en1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1', '48.bo1', '72.dh1'], 'contains': ['288.w1', '288.dk1', '288.dv1', '432.gg1', '432.hh1', '432.hk1', '432.hl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 325, 40323593520, 269279866800, 6227827200, 41091127], 'label': '46656.ir.144.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '144.en1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.en1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715763
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '6.i1', '6.o1'], 'contains': ['24.bo1', '24.bv1', '24.bx1', '36.cz1', '108.dc1', '108.el1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 6267744007, 1481684400, 1174320, 1174645, 7, 39957619, 269279866800], 'label': '46656.ir.12.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715764
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.eo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1', '72.bi1', '72.du1', '72.fy1'], 'contains': ['288.p1', '288.u1', '288.bk1', '432.gi1', '432.hr1', '432.hs1', '432.ht1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 6227827200, 104, 1174645], 'label': '46656.ir.144.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.eo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eo1', 'subgroup_fusion': None, 'weyl_group': '48.35'}
  • id: 216715765
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ep1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bj1', '72.bu1', '72.fz1', '72.ge1'], 'contains': ['288.r1', '288.bm1', '432.hs1', '432.hu1', '432.hv1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 269278773445, 1174320, 1481684400, 6227827200, 355419187304], 'label': '46656.ir.144.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '144.ep1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ep1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715766
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.eq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bj1', '72.bj1', '72.bv1', '72.ct1', '72.ga1', '72.gc1', '72.gf1', '72.gi1'], 'contains': ['288.s1', '288.bn1', '432.hr1', '432.hu1', '432.hv1', '432.hw1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.144.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.eq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eq1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 216715767
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.er1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bj1', '72.k1', '72.bw1', '72.dv1', '72.gb1', '72.gd1', '72.gg1', '72.gh1'], 'contains': ['288.v1', '288.bo1', '432.ht1', '432.hu1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 6227827200, 1174645], 'label': '46656.ir.144.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.er1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.er1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715768
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.es1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bk1', '48.bl1', '72.cu1'], 'contains': ['288.y1', '288.bc1', '288.bu1', '432.gl1', '432.go1', '432.hx1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [41091120, 554365249658, 325, 40323593520, 269279866800, 6227827200], 'label': '46656.ir.144.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bh1', 'old_label': '144.es1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.es1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 216715769
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.et1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '48.bl1', '72.ck1'], 'contains': ['288.z1', '288.bi1', '288.cb1', '432.gp1', '432.hx1'], 'core': '864.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [41091120, 39366316080, 624302466480, 1481684400, 269279866800, 6227827200], 'label': '46656.ir.144.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1', 'old_label': '144.et1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.et1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715770
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.eu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bm1', '48.bn1', '48.bo1', '72.cu1'], 'contains': ['288.y1', '288.cz1', '288.dp1', '432.hc1', '432.hh1', '432.hy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [554365249658, 325, 40323593520, 269279866800, 6227827200, 41091127], 'label': '46656.ir.144.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '144.eu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eu1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715771
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ev1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dp1', '48.bm1', '72.ck1'], 'contains': ['288.z1', '288.dc1', '288.dw1', '432.ho1', '432.hy1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 624302466480, 1481684400, 269279866800, 6227827200, 41091127], 'label': '46656.ir.144.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.ev1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ev1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715772
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ew1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bm1', '48.bn1'], 'contains': ['288.ba1', '288.dd1', '288.dy1', '432.hp1', '432.hy1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [624190336641, 1481684504, 40323593520, 269279866800, 6227827200, 41091127], 'label': '46656.ir.144.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ew1', 'old_label': '144.ew1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ew1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715773
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ex1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1', '72.de1'], 'contains': ['288.bb1', '288.cs1', '288.ec1', '432.hz1', '432.id1', '432.ie1', '432.ig1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 300933848880, 325, 382729979624, 457175461950, 6227827207], 'label': '46656.ir.144.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1', 'old_label': '144.ex1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ex1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715774
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.f1', '6.o1'], 'contains': ['24.bp1', '24.bq1', '24.bx1', '36.da1', '108.dd1', '108.em1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 499, 7, 6227464327, 269279866800], 'label': '46656.ir.12.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715775
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ey1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1', '72.e1', '72.bk1', '72.fv1', '72.gj1'], 'contains': ['288.bf1', '288.ce1', '288.cy1', '432.ia1', '432.ib1', '432.ij1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41091120, 268280812800, 325, 31658054504, 39957127, 37885034880], 'label': '46656.ir.144.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.ey1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ey1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715776
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ez1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1', '72.u1', '72.fu1', '72.fw1'], 'contains': ['288.be1', '288.cf1', '288.cw1', '432.ib1', '432.ic1', '432.ik1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 301891126320, 325, 1481684400, 1481684504, 39957127], 'label': '46656.ir.144.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.ez1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ez1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715777
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fa1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1', '72.l1', '72.v1', '72.bk1'], 'contains': ['288.bf1', '288.cg1', '288.cx1', '432.ia1', '432.ic1', '432.il1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 39957127], 'label': '46656.ir.144.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.fa1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fa1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715778
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1', '72.bl1', '72.cz1', '72.fw1'], 'contains': ['288.be1', '288.cj1', '288.eb1', '432.if1', '432.ig1', '432.ih1', '432.im1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 268280812800, 325, 6227827207, 104], 'label': '46656.ir.144.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.fb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fb1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715779
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bp1', '48.br1', '72.cu1'], 'contains': ['288.bc1', '288.cm1', '288.dp1', '432.id1', '432.ip1', '432.iq1', '432.ir1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [41091120, 554365249658, 325, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.144.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.cu1', 'old_label': '144.fc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fc1', 'subgroup_fusion': None, 'weyl_group': '648.555'}
  • id: 216715780
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bp1', '48.bs1'], 'contains': ['288.bd1', '288.cn1', '288.dq1', '432.ie1', '432.ip1', '432.ir1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [40323593624, 41091120, 40323593520, 269279866800, 455107081395, 6227827207], 'label': '46656.ir.144.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fd1', 'old_label': '144.fd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fd1', 'subgroup_fusion': None, 'weyl_group': '324.121'}
  • id: 216715781
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fe1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1', '72.bl1', '72.df1', '72.fu1'], 'contains': ['288.be1', '288.cp1', '288.dt1', '432.if1', '432.ii1', '432.in1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [40323593624, 41091120, 268280812800, 325, 40323593520, 6227827207], 'label': '46656.ir.144.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.fe1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fe1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715782
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ff1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1', '72.m1', '72.dg1', '72.fv1'], 'contains': ['288.bf1', '288.cq1', '288.du1', '432.ih1', '432.ii1', '432.io1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41091120, 39366316080, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.144.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.ff1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ff1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715783
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1', '48.bt1', '72.dh1'], 'contains': ['288.bg1', '288.cr1', '288.dv1', '432.ig1', '432.ii1', '432.ip1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [40323593624, 41091120, 325, 40323593520, 269279866800, 6227827207], 'label': '46656.ir.144.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cm1', 'old_label': '144.fg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fg1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715784
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bq1', '72.r1', '72.bm1', '72.fx1'], 'contains': ['288.bh1', '288.cd1', '288.cv1', '432.ij1', '432.ik1', '432.il1', '432.is1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 1481684504, 269279866800, 39957127], 'label': '46656.ir.144.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.fh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fh1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715785
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.h1', '6.m1'], 'contains': ['24.bp1', '24.bt1', '24.by1', '36.db1', '108.de1', '108.en1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 6267381127, 499, 7, 269279866800], 'label': '46656.ir.12.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715786
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.br1', '48.bs1', '48.bt1', '72.bn1', '72.cs1', '72.fx1'], 'contains': ['288.bh1', '288.ci1', '288.dn1', '432.im1', '432.in1', '432.io1', '432.ip1', '432.it1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684835, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.144.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1', 'old_label': '144.fi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fi1', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 216715787
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11664.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bu1', '48.br1', '72.ck1'], 'contains': ['288.bi1', '288.ck1', '288.dw1', '432.iq1', '432.it1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41091120, 39366316080, 624302466480, 1481684400, 269279866800, 6227827207], 'label': '46656.ir.144.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bw1', 'old_label': '144.fj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fj1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715788
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.bv1', '48.br1', '48.bs1'], 'contains': ['288.bj1', '288.cl1', '288.dx1', '432.ir1', '432.it1'], 'core': '864.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [41091120, 39366316080, 1481684400, 269279866800, 6227827207, 463289990028], 'label': '46656.ir.144.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.fk1', 'old_label': '144.fk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fk1', 'subgroup_fusion': None, 'weyl_group': '324.39'}
  • id: 216715789
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1', '72.bi1', '72.ei1', '72.gk1'], 'contains': ['288.bk1', '288.bp1', '288.by1', '432.iu1', '432.je1', '432.jf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 104, 1174645, 6267744000], 'label': '46656.ir.144.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.fl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fl1', 'subgroup_fusion': None, 'weyl_group': '144.143'}
  • id: 216715790
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1', '72.u1', '72.fy1', '72.gk1'], 'contains': ['288.bk1', '288.cf1', '288.di1', '432.iw1', '432.jg1', '432.jj1', '432.jl1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [301891126320, 39957120, 1134007, 325, 1481684400, 1521641624], 'label': '46656.ir.144.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.fm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fm1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715791
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1', '72.v1', '72.br1', '72.hg1'], 'contains': ['288.bl1', '288.cg1', '288.dj1', '432.iw1', '432.jh1', '432.ji1', '432.jk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 39957120, 1134007, 325, 1481684400, 1521641624], 'label': '46656.ir.144.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.fn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fn1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715792
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1', '72.bk1', '72.bq1', '72.hg1'], 'contains': ['288.bl1', '288.ce1', '288.cg1', '432.iv1', '432.jm1', '432.jn1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 325, 1481684400, 1521641624], 'label': '46656.ir.144.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.fo1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fo1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715793
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1', '72.bl1', '72.du1', '72.gk1'], 'contains': ['288.bk1', '288.cj1', '288.cp1', '432.ix1', '432.jo1', '432.jp1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39366316080, 268280812800, 1174320, 6227827207, 104, 1174645], 'label': '46656.ir.144.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.fp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fp1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715794
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1', '72.bk1', '72.br1', '72.fc1'], 'contains': ['288.bl1', '288.cx1', '288.cy1', '432.iy1', '432.jq1', '432.jr1', '432.js1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [41050807, 39366316080, 39957120, 325, 1481684400, 1521641624], 'label': '46656.ir.144.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '144.fq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fq1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715795
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1', '72.bl1', '72.ei1', '72.fy1'], 'contains': ['288.bk1', '288.dt1', '288.eb1', '432.iz1', '432.jt1', '432.ju1', '432.jv1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [6267744007, 39366316080, 268280812800, 1174320, 104, 1174645], 'label': '46656.ir.144.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.fr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fr1', 'subgroup_fusion': None, 'weyl_group': '1296.3524'}
  • id: 216715796
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.g1', '6.p1'], 'contains': ['24.bq1', '24.br1', '24.by1', '36.dc1', '108.df1', '108.ep1'], 'core': '48.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6267381738, 6227464327, 269279866800], 'label': '46656.ir.12.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.br1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715797
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1', '72.k1', '72.bx1', '72.er1', '72.gl1', '72.gm1', '72.gn1', '72.hf1'], 'contains': ['288.bo1', '288.bq1', '432.je1', '432.jy1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 1174645, 6267744000], 'label': '46656.ir.144.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.fs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fs1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715798
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ft1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bu1', '72.bj1', '72.by1', '72.cv1', '72.go1', '72.gp1', '72.gq1', '72.hj1'], 'contains': ['288.bn1', '288.bt1', '432.jf1', '432.jy1', '432.jz1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6267744000], 'label': '46656.ir.144.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.ft1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ft1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715799
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bv1', '72.bz1', '72.fz1', '72.gr1'], 'contains': ['288.bm1', '288.cc1', '288.df1', '432.jh1', '432.jj1', '432.ka1', '432.kb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [268280812800, 39957120, 1134007, 39366316405, 31697930984, 37885034880], 'label': '46656.ir.144.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '144.fu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fu1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715800
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bv1', '72.r1', '72.ca1', '72.ga1', '72.go1', '72.gs1', '72.gt1', '72.hl1'], 'contains': ['288.bn1', '288.cd1', '288.dg1', '432.jg1', '432.ji1', '432.ka1', '432.kb1', '432.kc1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1521641955, 39957120, 1134007, 1481684400, 269279866800], 'label': '46656.ir.144.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.fv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fv1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715801
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bv1', '72.e1', '72.cb1', '72.gb1', '72.gl1', '72.gu1', '72.gv1', '72.hg1'], 'contains': ['288.bo1', '288.ce1', '288.dj1', '432.jk1', '432.jl1', '432.ka1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 1134007, 325, 31697930984, 37885034880], 'label': '46656.ir.144.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.fw1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fw1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715802
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bw1', '72.bm1', '72.bs1', '72.gc1', '72.gp1', '72.gw1', '72.gx1', '72.hl1'], 'contains': ['288.bn1', '288.cd1', '432.jm1', '432.kd1', '432.ke1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39916807, 39366316080, 39957120, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.144.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.fx1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fx1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715803
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fy1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1', '72.l1', '72.bt1', '72.gd1', '72.gm1', '72.gy1', '72.gz1', '72.hg1'], 'contains': ['288.bo1', '288.cg1', '432.jn1', '432.ke1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39916807, 268280812800, 39957120, 325, 31697930984, 37885034880], 'label': '46656.ir.144.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.fy1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fy1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715804
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.fz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bx1', '72.bn1', '72.cc1', '72.ct1', '72.go1', '72.gw1', '72.ha1', '72.hm1'], 'contains': ['288.bn1', '288.ci1', '432.jo1', '432.kf1', '432.kg1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 269279866800, 6227827207], 'label': '46656.ir.144.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.fz1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fz1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715805
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ga1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1', '72.m1', '72.cd1', '72.dv1', '72.gl1', '72.gy1', '72.hb1', '72.hh1'], 'contains': ['288.bo1', '288.cq1', '432.jp1', '432.kg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 1481684504, 6227827207, 1174645], 'label': '46656.ir.144.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.ga1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ga1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715806
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.by1', '72.bz1', '72.ge1', '72.hc1'], 'contains': ['288.bm1', '288.cu1', '432.jq1', '432.kh1', '432.ki1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 39366316405, 31697930984, 37885034880], 'label': '46656.ir.144.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '144.gb1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gb1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715807
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.f1', '6.p1'], 'contains': ['24.bq1', '24.bs1', '24.bu1', '36.dd1', '108.dg1', '108.eo1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174320, 1174645, 7, 6227827818, 6227464327, 269279866800], 'label': '46656.ir.12.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1', 'subgroup_fusion': None, 'weyl_group': '5184.rx'}
  • id: 216715808
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.by1', '72.bm1', '72.ca1', '72.cy1', '72.gf1', '72.gq1', '72.ha1', '72.hd1'], 'contains': ['288.bn1', '288.cv1', '432.jr1', '432.kh1', '432.ki1', '432.kj1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [41050807, 39366316080, 1521641955, 39957120, 1481684400, 269279866800], 'label': '46656.ir.144.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.gc1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gc1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715809
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.by1', '72.l1', '72.cb1', '72.fc1', '72.gg1', '72.gn1', '72.hb1', '72.he1'], 'contains': ['288.bo1', '288.cx1', '432.js1', '432.kh1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [41050807, 268280812800, 39957120, 325, 31697930984, 37885034880], 'label': '46656.ir.144.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.gd1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gd1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715810
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.ge1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bz1', '72.ce1', '72.fz1', '72.hc1'], 'contains': ['288.bm1', '288.dm1', '432.ju1', '432.kk1', '432.kl1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [6267744007, 39366316080, 269278773445, 1174320, 1481684400, 355419187304], 'label': '46656.ir.144.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '144.ge1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ge1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715811
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.bz1', '72.bn1', '72.cf1', '72.cv1', '72.ga1', '72.gx1', '72.hd1', '72.hp1'], 'contains': ['288.bn1', '288.dn1', '432.jt1', '432.kk1', '432.kl1', '432.km1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.144.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.gf1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gf1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715812
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bz1', '72.m1', '72.cg1', '72.er1', '72.gb1', '72.gz1', '72.he1', '72.hi1'], 'contains': ['288.bo1', '288.du1', '432.jv1', '432.kk1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267744007, 39366316080, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.144.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.gg1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gg1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715813
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ca1', '72.bu1', '72.gr1', '72.hc1'], 'contains': ['288.bm1', '432.kn1', '432.kr1', '1296.jb1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39366316080, 270715783064, 6227464320, 1481684400, 1174320, 1174645], 'label': '46656.ir.144.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.t1', 'old_label': '144.gh1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gh1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
  • id: 216715814
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cd1', '72.ce1', '72.ge1', '72.gr1'], 'contains': ['288.bm1', '432.kq1', '432.ks1', '1296.jc1'], 'core': '46656.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39366316080, 6267381127, 269278773445, 1174320, 1481684400, 355419187304], 'label': '46656.ir.144.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bi1', 'old_label': '144.gi1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gi1', 'subgroup_fusion': None, 'weyl_group': '1296.3527'}
  • id: 216715815
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ca1', '72.bo1', '72.bv1', '72.cw1', '72.gs1', '72.gw1', '72.hd1', '72.hj1'], 'contains': ['288.bn1', '432.kn1', '432.kr1', '432.kt1', '1296.ix1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39366316080, 6227464320, 1174320, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.144.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.gj1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gj1', 'subgroup_fusion': None, 'weyl_group': '288.1031'}
  • id: 216715816
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cb1', '72.bo1', '72.by1', '72.cx1', '72.gi1', '72.gt1', '72.gx1', '72.ha1'], 'contains': ['288.bn1', '432.ko1', '432.ku1', '1296.iy1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.144.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.gk1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gk1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715817
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15552.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cc1', '72.bp1', '72.cc1', '72.cw1', '72.gc1', '72.gq1', '72.gt1', '72.hp1'], 'contains': ['288.bn1', '432.kp1', '432.kv1', '1296.iz1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 1481684835, 1174320, 1481684400, 6227464327, 269279866800], 'label': '46656.ir.144.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.gl1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gl1', 'subgroup_fusion': None, 'weyl_group': '864.4686'}
  • id: 216715818
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.g1', '6.o1'], 'contains': ['24.bq1', '24.bv1', '24.bw1', '36.de1', '108.dh1', '108.eq1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1481684504, 1481684400, 1174645, 1174320, 7, 39957619, 6227464327, 269279866800], 'label': '46656.ir.12.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1', 'subgroup_fusion': None, 'weyl_group': '15552.lz'}
  • id: 216715819
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '46656.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cd1', '72.bp1', '72.cf1', '72.cx1', '72.gf1', '72.gp1', '72.gs1', '72.hm1'], 'contains': ['288.bn1', '432.kq1', '432.ks1', '432.kw1', '1296.ja1'], 'core': '1728.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 269279866800], 'label': '46656.ir.144.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1', 'old_label': '144.gm1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gm1', 'subgroup_fusion': None, 'weyl_group': '2592.fs'}
  • id: 216715820
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ca1', '72.n1', '72.bw1', '72.et1', '72.gu1', '72.gy1', '72.he1', '72.hf1'], 'contains': ['288.bo1', '432.kn1', '1296.jd1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 6227464320, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.144.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.gn1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gn1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715821
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.go1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cb1', '72.n1', '72.bx1', '72.ew1', '72.gh1', '72.gv1', '72.gz1', '72.hb1'], 'contains': ['288.bo1', '432.ko1', '1296.je1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6267381120, 39366316080, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.144.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.go1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.go1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715822
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cc1', '72.o1', '72.cd1', '72.et1', '72.gd1', '72.gn1', '72.gv1', '72.hi1'], 'contains': ['288.bo1', '432.kp1', '1296.jf1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [39366316080, 1174320, 1481684400, 6227464327, 1481684504, 1174645], 'label': '46656.ir.144.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.gp1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gp1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715823
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '23328.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cd1', '72.o1', '72.cg1', '72.ew1', '72.gg1', '72.gm1', '72.gu1', '72.hh1'], 'contains': ['288.bo1', '432.kq1', '1296.jg1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [39366316080, 6267381127, 1174320, 1481684400, 1481684504, 1174645], 'label': '46656.ir.144.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.gq1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gq1', 'subgroup_fusion': None, 'weyl_group': '2592.ft'}
  • id: 216715824
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1', '72.ch1', '72.fc1', '72.gh1', '72.hf1', '72.hg1', '72.hh1', '72.hi1'], 'contains': ['288.bl1', '288.bo1', '432.jx1', '432.kx1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [268280812800, 39957120, 41050800, 41051125, 31697930984, 37885034880], 'label': '46656.ir.144.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '144.gr1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gr1', 'subgroup_fusion': None, 'weyl_group': '288.877'}
  • id: 216715825
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.d1', '48.ce1', '48.cf1', '72.ci1', '72.cy1', '72.gi1', '72.hj1', '72.hl1', '72.hm1', '72.hp1'], 'contains': ['288.bn1', '432.a1', '432.kx1'], 'core': '432.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39366316080, 39957120, 41050800, 1481684400, 269279866800, 1521641624], 'label': '46656.ir.144.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '144.gs1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gs1', 'subgroup_fusion': None, 'weyl_group': '2592.cg'}
  • id: 216715826
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ce1', '48.cf1', '72.cj1', '72.ho1', '72.hr1'], 'contains': ['432.a1', '576.q1', '3888.fw1'], 'core': '432.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [462923481264, 39366316080, 39957120, 41050800, 1481684400, 269279866800], 'label': '46656.ir.144.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '144.gt1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gt1', 'subgroup_fusion': None, 'weyl_group': '1296.3490'}
  • id: 216715827
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1', '72.d1', '72.fv1', '72.gl1'], 'contains': ['288.bq1', '288.ce1', '288.cq1', '432.ky1', '432.lb1', '432.ld1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 325, 1481684400, 1481684504, 6227827207], 'label': '46656.ir.144.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '144.gu1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gu1', 'subgroup_fusion': None, 'weyl_group': '432.753'}
  • id: 216715828
    {'ambient': '46656.ir', 'aut_centralizer_order': None, 'aut_label': '144.gv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7776.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cg1', '72.s1', '72.fw1', '72.gk1'], 'contains': ['288.bp1', '288.cf1', '288.cj1', '432.ky1', '432.lc1', '432.le1'], 'core': '5184.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39916807, 39366316080, 268280812800, 325, 6227827207, 104], 'label': '46656.ir.144.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '144.gv1', 'projective_image': '46656.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gv1', 'subgroup_fusion': None, 'weyl_group': '432.753'}